Implicit Differentiation - GRE Quantitative Reasoning
Card 0 of 16
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
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
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
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