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

Albarellak

Answered question

2021-03-26

Find the first partial derivatives of the following functions.

g (x, y) = \cos^{5} (x^{2} y^{3})

komunidadO

Skilled2021-03-28Added 86 answers

Step 1
To find the partial derivatives.

g (x, y) = \cos^{5} (x^{2} y^{3})

Step 2
Let us first evaluate the partial derivative with respect to x.
We differentiate the function with respect to x keeping y constant.

\frac{\partial g (x, y)}{\partial x} = 5 \cos^{4} (x^{2} y^{3}) (- \sin (x^{2} y^{3})) (2 x y^{3})

(Chain Rule of differentiation is also applicable)

= - 10 x y^{3} \cos^{4} (x^{2} y^{3}) \sin (x^{2} y^{3})

Step 3
Now, let us evaluate the partial derivative with respect to y.
We differentiate the function with respect to y keeping x constant.

\frac{\partial g (x, y)}{\partial y} = 5 \cos^{4} (x^{2} y^{3}) (- \sin (x^{2} y^{3})) (3 x^{2} y^{2})

(Chain Rule of differentiation is also applicable)

= - 15 x^{2} y^{2} \cos^{4} (x^{2} y^{3}) \sin (x^{2} y^{3})

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?