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Example Questions
Example Question #1041 : Partial Derivatives
Find
of the following function:
To find the given partial derivative of the function, we must treat the other variable(s) as constants. For higher order partial derivatives, we work from left to right for the given variables.
First, we must find the partial derivative of the function with respect to x:
Then, we find the partial derivative of this function with respect to x:
Example Question #1042 : Partial Derivatives
Find
of the function
To find
of the function, you take three consecutive partial derivatives:
Example Question #1043 : Partial Derivatives
Find
of the function
To find
of the function, you must take three consecutive partial derivatives:
Example Question #1044 : Partial Derivatives
Find
given
To find
we take the derivative of the function with respect to and treat the other variables as constants.As such,
yields
Example Question #1045 : Partial Derivatives
Find
given
To find
we take the derivative of the function with respect to and treat the other variables as constants.As such,
yields
Example Question #1042 : Partial Derivatives
Find
given
To find
we take the derivative of the function with respect to and treat the other variables as constants.As such,
yields
Example Question #1047 : Partial Derivatives
Find
of the following function:
To find the given partial derivative of the function, we must treat the other variable(s) as constants. For higher order partial derivatives, we work from left to right for the given variables.
First, we must find the partial derivative of the function with respect to y:
Next, we find the partial derivative of this function with respect to z:
Now, we find the partial derivative of this function with respect to y:
Finally, we take the partial derivative of this function with respect to z:
Example Question #1042 : Partial Derivatives
Find
of the function
To find
of the function, you must take two consecutive partial derivatives:
Example Question #3411 : Calculus 3
Find
of the function
To find
of the function, you must take two consecutive partial derivatives:
Example Question #1052 : Partial Derivatives
Calculate the partial derivative with respect to
of the following function:
When calculating the partial derivative with respect to the variable
of a function of more than one variable, apply the standard rules for differentiating a function of a single variable, and treat the other variables as constants. In this case, we have:
We are being asked to differentiate
with respect to , so we treat the variable as a constant and apply the sum and quotient rules of differentiation to find the partial derivative , as shown:
Since
is treated as a constant, we can factor out from the sum of these two terms and simplify the expression:
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