Best solutions to - "Find the first partial derivatives of the given..."

amanf

Answered question

2021-10-09

Find the first partial derivatives of the given functions.
$F i n d \frac{\partial f}{\partial x} if f (x, y) = y \sin x y$

funblogC

Skilled2021-10-10Added 91 answers

Step 1
Given:

f (x, y) = y \sin (x y)

Step 2
Concept:
When we partial derivative any function with respect to any variable then other variables are treated as constant
Step 3
Solution:

f (x, y) = y \sin (x y)

Partial derivative with respect to x keeping y constant

\frac{\partial f}{\partial x} = \frac{\partial}{\partial x} (y \sin (x y))

\frac{\partial f}{\partial x} = y \frac{\partial}{\partial x} (\sin (x y))

\frac{\partial f}{\partial x} = y \cos (x y) \frac{\partial}{\partial x} (x y)

\frac{\partial f}{\partial x} = y \cos (x y) (y)

\frac{\partial f}{\partial x} = y^{2} \cos (x y)

Step 4
Answer:

\frac{\partial f}{\partial x} = y^{2} \cos (x y)

Jeffrey Jordon

Expert2022-03-13Added 2605 answers

Answer is given below (on video)

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