Question

Can someone please help me find the derivative of this problem? I will fan and medal.

Answer 1

Whats the function?

Answer 2

I'm typing it

Answer 3

\[\frac{ 2 }{ 3 }\sin^\frac{ 3 }{ 2 }x-\frac{ 2 }{ 7 }\sin^\frac{ 7 }{ 2 }x\]

Answer 4

\[\frac{2}{3}\left(\sin^{2/3}x\right)' \iff \frac{2}{3}\left((\sin(x))^{2/3}\right)'\]

Answer 5

If you look carefully you see that the two functions are connected with the subtract sign. So you can break that function into 2 separate derivatives.

Answer 6

\[\frac{ d }{ dx } (\frac{ 2 }{ 3 }\sin ^{2/3}(x)) - \frac{ d }{ dx }((\frac{ 2 }{ 7 }\sin ^{7/2}x))\]

Answer 7

Use the power rule, then the chain rule.