(partial y)/(partial y)(x^2+y^2)^2

Question

Answer 1

To find the partial derivative of

with respect to

in the expression \( (x^2 + y^2)^2 \), we can use the chain rule. Let's break it down step by step.Given:

We need to find:

First, let's rewrite the function in terms of

:

Now, apply the chain rule. The outer function is

and the inner function is

.1. Differentiate the outer function with respect to the inner function:

2. Differentiate the inner function with respect to

:

Now, combine these results using the chain rule:

Simplify:

So, the partial derivative of \( (x^2 + y^2)^2 \) with respect to

is:

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