find h'(0) if h(x)=[5x^2-4g(x)][g(x)+5x] where g (0) =5 and g'(0)=2

Answer 1

Hi Jayna,

Let me see if I can help you get to the answer.

Recall, the product rule of derivatives:

If h(x) = f(x)g(x)

then h'(x) = f(x)g'(x) + f'(x)g(x)

For example, let's say we have,

h(x) = (x³ + 4x)(sin(x))

Then,

h'(x) = (x³ + 4x)(cos(x)) + (3x² + 4)(sin(x))

It seems like we have the product of two functions in your question. Only in this case, the functions being multiplied are 5x² - 4g(x) and g(x) + 5x.

Let me know if this helps you.