f (x) =(x^2-3)(5×^2-1)

Question

How to solve using the product rule

Answer 1

????????????? "produkt rule" ????????????

??????? yu wanna MULTIPLI ?????????

(x^2-3)*(5x^2-1)=5x^4 -16x^2 +3

Answer 2

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))