Question

Let
f(x)=(4 x²-4)⁸(-4 x²-8)¹1
Give your derivative in factored form
fʹ(x)=__

Answer 1

To find the derivative of the given function f(x) = (4x²-4)⁸(-4x²-8)¹¹, apply the product rule and simplify the expression.

Step-by-step explanation:

The given function is f(x) = (4x²-4)⁸(-4x²-8)¹¹. To find the derivative of this function, we can apply the product rule. The product rule states that if we have a function f(x) = g(x)h(x), then the derivative of f(x) with respect to x is given by f'(x) = g'(x)h(x) + g(x)h'(x).

So, applying the product rule to the given function, we have:

f'(x) = 8(4x²-4)⁷(-4x²-8)¹¹ + (4x²-4)⁸(11)(-8x-8)

Simplifying further, we get:

f'(x) = 32(4x²-4)⁷(-4x²-8)¹¹ - 44(4x²-4)⁸(x+1)