f(x) = x^3*g(x) , g(-7) = 2 , g'(-7) = -9 . What is f'(7) ?

Question

anonymous · Answer

apply multiplication rule for derivatives
i dont remember that actual name for it

anonymous · Answer

use the chain rule to find derivative of f(x)

anonymous · Answer

"product rule"

anonymous · Answer

$$f \left( x \right)= x^3 \times g \left( x \right) $$
you mean this?

3psilon · Answer

yes

anonymous · Answer

$$f \prime \left( x \right)= x^3 \times \left( \frac{ d }{ dx } \right)g \left( x \right) + g \left( x  \right) \times \left( \frac{ d }{ dx } \right)x^3$$

anonymous · Answer

$$f \prime \left( x \right)= x^3 \times g \prime \left( x \right) + g \left( x \right) \times 2x^2$$

anonymous · Answer

$$f \prime \left( x \right)= x^3 \times g \prime \left( x \right) + g \left( x \right) \times 3x^2$$
this one

anonymous · Answer

now to find
$$f \prime \left( 7 \right) =7^3 \times \left( -9 \right) + 2 \times \left( 3 \times7^2 \right)$$

anonymous · Answer

what is g(7), only know g(-7)