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3psilon
f(x) = x^3*g(x) , g(-7) = 2 , g'(-7) = -9 . What is f'(7) ?
apply multiplication rule for derivatives i dont remember that actual name for it
use the chain rule to find derivative of f(x)
\[f \left( x \right)= x^3 \times g \left( x \right) \] you mean this?
\[f \prime \left( x \right)= x^3 \times \left( \frac{ d }{ dx } \right)g \left( x \right) + g \left( x \right) \times \left( \frac{ d }{ dx } \right)x^3\]
\[f \prime \left( x \right)= x^3 \times g \prime \left( x \right) + g \left( x \right) \times 2x^2\]
\[f \prime \left( x \right)= x^3 \times g \prime \left( x \right) + g \left( x \right) \times 3x^2\] this one
now to find \[f \prime \left( 7 \right) =7^3 \times \left( -9 \right) + 2 \times \left( 3 \times7^2 \right)\]
what is g(7), only know g(-7)