Question

Compute the partial derivatives of z = 8x/√(x²+y²).

Answer 1

To compute the partial derivatives of the given function z = 8x/√(x²+y²), differentiate the function with respect to each variable separately. The partial derivative with respect to x is 8/√(x²+y²) - (8x²)/(x²+y²), and the partial derivative with respect to y is (-8xy)/(x²+y²).

Step-by-step explanation:

To compute the partial derivatives of the given function z = 8x/√(x²+y²), we need to differentiate it with respect to each variable separately. Let's start with respect to x:

∂z/∂x = 8/√(x²+y²) - (8x)(1/2)(2x)/(2√(x²+y²)³)

Simplifying this expression, we get:

∂z/∂x = 8/√(x²+y²) - (8x²)/(x²+y²)

Now, let's find the partial derivative with respect to y:

∂z/∂y = (-8x)(1/2)(2y)/(2√(x²+y²)³)

This can be simplified to:

∂z/∂y = (-8xy)/(x²+y²)