Question

y=[x+(x+sin^2x)^5]^6

Answer 1

i need to find the derivative

Answer 2

y=[x+(x+sin^2x)^5]^6
y'=6(x+(x+sin^2x)^5)^5(1+5(x+sin^2x)^4(1+4sin2xcos2x))

Answer 3

can you please explain to me what you did

Answer 4

chain rule f(x)=u^6, f'(x)=6u^5u'
u=[x+(x+sin^2x)^5]
so f'(x)=6[x+(x+sin^2x)^5]^5[x+(x+sin^2x)^5]'

Answer 5

[x+(x+sin^2x)^5]'
need derivative again (1+5(x+sin^2x)^4(x+sin^2x)'
this time (x+sin^2x)'=(1+2sinxcosx)=(1+sin2x)