Partial Differentiation - GRE Quantitative Reasoning
Card 0 of 28
Solve for
: 
Solve for :
To solve for the partial derivative, let all other variables be constants besides the variable that is derived with respect to.
In
, the terms
are constants.
Derive as accordingly by the differentiation rules.

To solve for the partial derivative, let all other variables be constants besides the variable that is derived with respect to.
In , the terms
are constants.
Derive as accordingly by the differentiation rules.
Compare your answer with the correct one above
Suppose the function
. Solve for
.
Suppose the function . Solve for
.
Identify all the constants in function
.
Since we are solving for the partial differentiation of variable
, all the other variables are constants. Solve each term by differentiation rules.

Identify all the constants in function .
Since we are solving for the partial differentiation of variable , all the other variables are constants. Solve each term by differentiation rules.
Compare your answer with the correct one above
Suppose the function
. Solve for
.
Suppose the function . Solve for
.
Identify all the constants in function
.
Since we are solving for the partial differentiation of variable
, all the other variables are constants. Solve each term by differentiation rules.

Identify all the constants in function .
Since we are solving for the partial differentiation of variable , all the other variables are constants. Solve each term by differentiation rules.
Compare your answer with the correct one above
Find
for
.
Find
for
.
Our first step would be to differentiate both sides with respect to
:

The functions of
can be differentiated with respect to
, just remember to multiply by
.



Our first step would be to differentiate both sides with respect to :
The functions of can be differentiated with respect to
, just remember to multiply by
.
Compare your answer with the correct one above
Differentiate the following to solve for
.

Differentiate the following to solve for .
Our first step is to differentiate both sides with respect to
:

The functions of
can by differentiated with respect to
, just remember to multiply them by
:




Our first step is to differentiate both sides with respect to :
The functions of can by differentiated with respect to
, just remember to multiply them by
:
Compare your answer with the correct one above
Differentiate the following with respect to
.

Differentiate the following with respect to .
The first step is to differentiate both sides with respect to
:

Note: Those that are functions of
can be differentiated with respect to
, just remember to mulitply it by 

Now we can solve for
:




The first step is to differentiate both sides with respect to :
Note: Those that are functions of can be differentiated with respect to
, just remember to mulitply it by
Now we can solve for :
Compare your answer with the correct one above
Differentiate the following with respect to
.

Differentiate the following with respect to .
Our first step is to differentiate both sides with respect to
:

Note: we can differentiate the terms that are functions of
with respect to
, just remember to multiply it by
.

Note: The product rule was applied above:




Our first step is to differentiate both sides with respect to :
Note: we can differentiate the terms that are functions of with respect to
, just remember to multiply it by
.
Note: The product rule was applied above:
Compare your answer with the correct one above
Solve for
: 
Solve for :
To solve for the partial derivative, let all other variables be constants besides the variable that is derived with respect to.
In
, the terms
are constants.
Derive as accordingly by the differentiation rules.

To solve for the partial derivative, let all other variables be constants besides the variable that is derived with respect to.
In , the terms
are constants.
Derive as accordingly by the differentiation rules.
Compare your answer with the correct one above
Suppose the function
. Solve for
.
Suppose the function . Solve for
.
Identify all the constants in function
.
Since we are solving for the partial differentiation of variable
, all the other variables are constants. Solve each term by differentiation rules.

Identify all the constants in function .
Since we are solving for the partial differentiation of variable , all the other variables are constants. Solve each term by differentiation rules.
Compare your answer with the correct one above
Suppose the function
. Solve for
.
Suppose the function . Solve for
.
Identify all the constants in function
.
Since we are solving for the partial differentiation of variable
, all the other variables are constants. Solve each term by differentiation rules.

Identify all the constants in function .
Since we are solving for the partial differentiation of variable , all the other variables are constants. Solve each term by differentiation rules.
Compare your answer with the correct one above
Find
for
.
Find
for
.
Our first step would be to differentiate both sides with respect to
:

The functions of
can be differentiated with respect to
, just remember to multiply by
.



Our first step would be to differentiate both sides with respect to :
The functions of can be differentiated with respect to
, just remember to multiply by
.
Compare your answer with the correct one above
Differentiate the following to solve for
.

Differentiate the following to solve for .
Our first step is to differentiate both sides with respect to
:

The functions of
can by differentiated with respect to
, just remember to multiply them by
:




Our first step is to differentiate both sides with respect to :
The functions of can by differentiated with respect to
, just remember to multiply them by
:
Compare your answer with the correct one above
Differentiate the following with respect to
.

Differentiate the following with respect to .
The first step is to differentiate both sides with respect to
:

Note: Those that are functions of
can be differentiated with respect to
, just remember to mulitply it by 

Now we can solve for
:




The first step is to differentiate both sides with respect to :
Note: Those that are functions of can be differentiated with respect to
, just remember to mulitply it by
Now we can solve for :
Compare your answer with the correct one above
Differentiate the following with respect to
.

Differentiate the following with respect to .
Our first step is to differentiate both sides with respect to
:

Note: we can differentiate the terms that are functions of
with respect to
, just remember to multiply it by
.

Note: The product rule was applied above:




Our first step is to differentiate both sides with respect to :
Note: we can differentiate the terms that are functions of with respect to
, just remember to multiply it by
.
Note: The product rule was applied above:
Compare your answer with the correct one above
Solve for
: 
Solve for :
To solve for the partial derivative, let all other variables be constants besides the variable that is derived with respect to.
In
, the terms
are constants.
Derive as accordingly by the differentiation rules.

To solve for the partial derivative, let all other variables be constants besides the variable that is derived with respect to.
In , the terms
are constants.
Derive as accordingly by the differentiation rules.
Compare your answer with the correct one above
Suppose the function
. Solve for
.
Suppose the function . Solve for
.
Identify all the constants in function
.
Since we are solving for the partial differentiation of variable
, all the other variables are constants. Solve each term by differentiation rules.

Identify all the constants in function .
Since we are solving for the partial differentiation of variable , all the other variables are constants. Solve each term by differentiation rules.
Compare your answer with the correct one above
Suppose the function
. Solve for
.
Suppose the function . Solve for
.
Identify all the constants in function
.
Since we are solving for the partial differentiation of variable
, all the other variables are constants. Solve each term by differentiation rules.

Identify all the constants in function .
Since we are solving for the partial differentiation of variable , all the other variables are constants. Solve each term by differentiation rules.
Compare your answer with the correct one above
Find
for
.
Find
for
.
Our first step would be to differentiate both sides with respect to
:

The functions of
can be differentiated with respect to
, just remember to multiply by
.



Our first step would be to differentiate both sides with respect to :
The functions of can be differentiated with respect to
, just remember to multiply by
.
Compare your answer with the correct one above
Differentiate the following to solve for
.

Differentiate the following to solve for .
Our first step is to differentiate both sides with respect to
:

The functions of
can by differentiated with respect to
, just remember to multiply them by
:




Our first step is to differentiate both sides with respect to :
The functions of can by differentiated with respect to
, just remember to multiply them by
:
Compare your answer with the correct one above
Differentiate the following with respect to
.

Differentiate the following with respect to .
The first step is to differentiate both sides with respect to
:

Note: Those that are functions of
can be differentiated with respect to
, just remember to mulitply it by 

Now we can solve for
:




The first step is to differentiate both sides with respect to :
Note: Those that are functions of can be differentiated with respect to
, just remember to mulitply it by
Now we can solve for :
Compare your answer with the correct one above