Question: "Find the first partial derivatives of the following..."

djeljenike

Answered question

2021-06-03

Find the first partial derivatives of the following functions.

h (x, y, z) = \cos (x + y + z)

StrycharzT

Skilled2021-06-04Added 102 answers

Step 1
Consider the given function

h (x, y, z) = \cos (x + y + z)

Step 2
Now find the partial derivative with respect to x

\frac{\partial}{\partial x} (h (x, y, z)) = \frac{\partial}{\partial x} \cos (x + y + z)

= - \sin (x + y + z) \cdot \frac{\partial}{\partial x} (x + y + z)

= - \sin (x + y + z) \cdot (1 + 0 + 0)

= - \sin (x + y + z)

Step 3
Now find the partial derivative with respect to y

\frac{\partial}{\partial y} (h (x, y, z)) = \frac{\partial}{\partial x} \cos (x + y + z)

= - \sin (x + y + z) \cdot \frac{\partial}{\partial y} (x + y + z)

= - \sin (x + y + z) \cdot (0 + 1 + 0)

= - \sin (x + y + z)

Step 4
Now find the partial derivative with respect to z

\frac{\partial}{\partial z} (h (x, y, z)) = \frac{\partial}{\partial x} \cos (x + y + z)

= - \sin (x + y + z) \cdot \frac{\partial}{\partial z} (x + y + z)

= - \sin (x + y + z) \cdot (0 + 0 + 1)

= - \sin (x + y + z)

Jeffrey Jordon

Expert2021-11-20Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?