Explained: "First Partial Derivatives Given z = f(x)g( y),..."

Phoebe

Answered question

2021-10-05

First Partial Derivatives Given z = f(x)g( y), find

z_{x} + z_{y}

unessodopunsep

Skilled2021-10-06Added 105 answers

Step 1
Given function z=f(x)g(y).
When we find Partial derivative with respect to x then y will be termed as constant.

\frac{\partial}{\partial x} (f (x, y)) = f_{x} (x, y)

= z_{x}

And when we find partial derivative with respect to y then x will be termed as constant.

\frac{\partial}{\partial y} (f (x, y)) = f_{y} (x, y)

= z_{y}

Step 2
Partial derivative of given function with respect to x,

\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} [f (x) g (y)]

z_{x} = g (y) f^{'} (x)

Partial derivative of given function with respect to y,

\frac{\partial z}{\partial y} = \frac{\partial}{\partial y} [f (x) g (y)]

z_{y} = f (x) g^{'} (y)

Hence,

z_{x} + z_{y} = g (y) f^{'} (x) + f (x) g^{'} (y)

Jeffrey Jordon

Expert2022-11-15Added 2605 answers

Answer is given below (on video)

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