Question

Find the derivative of h(x) = (x² + 8)⁷ˣ

Answer 1

To find the derivative of h(x) = (x² + 8)⁷ˣ, use the chain rule and find the derivatives of the base function and the exponent. Then, apply the chain rule to get the derivative h'(x) = 14x(x² + 8)^(7x-1).

Step-by-step explanation:

To find the derivative of the function h(x) = (x² + 8)⁷ˣ, we can use the chain rule. Let's start by rewriting the function using exponential notation:

h(x) = (x² + 8)^(7x)

Now, let's find the derivative:

1. Take the derivative of the base function (x² + 8):
2. f(x) = x² + 8
3. f'(x) = 2x
4. Take the derivative of the exponent (7x):
5. g(x) = 7x
6. g'(x) = 7
7. Use the chain rule to find the derivative of the entire function:
8. h'(x) = g(x) * f'(g(x))
9. h'(x) = 7 * (x² + 8)^(7x-1) * 2x
10. h'(x) = 14x(x² + 8)^(7x-1)