Question

Use the chain rule to find the derivative of
8 √(5 x⁴+8 x⁵)

Answer 1

To find the derivative of 8 √(5x⁴+8x⁵) using the chain rule, we break down the problem into the derivative of the outer and inner functions, then multiply them together.

Step-by-step explanation:

To find the derivative of 8 √(5x⁴+8x⁵) using the chain rule, we need to apply the rule to the composite function. Let's break it down:

We have an outer function, which is the square root function, and an inner function, which is (5x⁴+8x⁵). The derivative of the outer function will be (1/2)(5x⁴+8x⁵)^(-1/2). The derivative of the inner function with respect to x will be 20x³+40x⁴.

Now, we can multiply the derivatives of the outer and inner functions:

(1/2)(5x⁴+8x⁵)^(-1/2) * (20x³+40x⁴)

Simplifying this expression will give us the final answer for the derivative.