Resolved: "Find all first partial derivatives. f(x,y)=excos⁡y" - Plainmath

jernplate8

Answered question

2021-02-19

Find all first partial derivatives.

f (x, y) = e^{x} \cos y

Answer & Explanation

Talisha

Skilled2021-02-21Added 93 answers

Step 1
Given:

f (x, y) = e^{x} \cos y

We know that for any given function f(x,y)=g(x)h(y)
All partial derivative is given by

\frac{\partial}{\partial x} (f (x, y)) = h (y) g^{'} (x)

and

\frac{\partial}{\partial y} (f (x, y)) = g (x) h^{'} (y)

Step 2
So,

\frac{\partial}{\partial x} (e^{x} \cos y) = \cos y e^{x} (u s e \frac{d}{d x} (e^{x}) = e^{x})

and

\frac{\partial}{\partial y} (e^{x} \cos y) = e^{x} . (- \sin y) (U s e \frac{d}{d x} (\cos x) = - \sin x)

\frac{\partial}{\partial y} (e^{x} \cos y) = - e^{x} \sin y

Hence,

\frac{\partial}{\partial x} (f (x, y)) and \frac{\partial}{\partial y} (f (x, y))

are respectively

e^{x} \cos y and - e^{x} \sin y

.

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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