Question

find the derivatives of g(x)=x^4(5x-3)^-2

Answer 1

\[g(x)={x^4 \over (5x-3)^{2}}\]

yes?

if so, quitient rule is a very standard approach

\[ \left( \dfrac{u}{v}\right)' = \dfrac{u' v - uv'}{v^2}\]

\[u = x^4, \qquad v = (5x-3)^2\]

Answer 2

You could also use the product rule on this one.
\[g(x)=x ^{4}(5x-3)^{-2}\]
Product rule:
\[(uv)\prime=uv \prime+vu\]
let's make u=\[x^{4}\] and v=\[(5x+3)^{-2}\]
Therefore, you would do \[x ^{4}(-10)(5x+3)+(5x+3)^{-2}4x ^{3}\]
After simplifying and combining like terms, and all that stuff, you would have your answer!

Answer 3

the vu in the product rule is supposed to say \[vu \prime\] sorry if that was confusing