Question

Derivative of this function.?

Could someone please show and explain step by step how to take this derivative

(2x^3 -3)^5
over
10

Answer 1

I need the anti derivative sorry

Answer 2

\[\int\frac{(2x^3-3)^5}{10}~dx\]
It'll be tedious, but expanding the binomial is the way to go:
\[(2x^3-3)^5=32x^{15}-240x^{12}+720x^{9}-1080x^{6}+810x^{3}-243\]
\[\frac{1}{10}\int\left(32x^{15}-240x^{12}+720x^{9}-1080x^{6}+810x^{3}-243\right)~dx\]
If there's a simpler way, I'm not seeing it right away.