"Find both first partial derivatives. z=sin⁡(5x)cos⁡(5y)" was answered by our community

Lipossig

Answered question

2021-04-19

Find both first partial derivatives.

z = \sin (5 x) \cos (5 y)

Brighton

Skilled2021-04-21Added 103 answers

Step 1
The given function is

z = \sin (5 x) \cos (5 y)

Differentiate the above equation partially with respect to x as follows.

\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} [\sin (5 x) \cos (5 y)]

= \cos (5 y) \frac{\partial}{\partial x} [\sin (5 x)]

= \cos (5 y) (5 \cos (5 x))

= 5 \cos (5 x) \cos (5 y)

Step 2
Differentiate the above equation partially with respect to y as follows.

\frac{\partial z}{\partial y} = \frac{\partial}{\partial y} [\sin (5 x) \cos (5 y)]

= \sin (5 x) \frac{\partial}{\partial x} [\cos (5 y)]

= \sin (5 x) (- 5 \sin (5 y))

= - 5 \sin (5 x) \sin (5 y)

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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