f(x)=(x²-3)(5x²-1) This problem is expressed as the product of 2 different functions.
Let f(x)=g(x)·h(x), where g(x)=x²-3 and h(x)=5x²-1, so that g'(x)=2x and h'(x)=10x
Both functions, g(x) and h(x), are differentiable at x, so we use the formula of product rule for the derivative of f(x) shown bellow.
f'(x)=(g(x)·h(x))'=g'(x)·h(x)+g(x)·h'(x) Therefore, we have:
f'(x)=2x·(5x²-1)+(x²-3)·10x Remove the brackets.
The answer is: f'(x)=20x³-32x (=4x·(√5·x + √8)·(√5·x - √8))