Question

What is the derivative of y=[x + (x + sin(x)^2)^6]^3 ?

Answer 1

\[\Large\rm y=\left[x+(x+\sin^2x)^6\right]^3\]Derivative of this?

Answer 2

well use General Power Rule!
\((U^n)'=nU^{n-1}U'\)
set \(U=x+(x+sin^2x)^6\)
\(U'=1+((x+sin^2x)^6)'\)
Chain rule again
\(6(x+sin^2x)^{5}(1+2cosxsinx)\)
then \(U'=1+6(x+sin^2x)^{5}(1+2cosxsinx)\)

Answer 3

Substitute U in the first line

Answer 4

and U' and you are done