chain rule

[mikeb]

Find f ' (x):

f(x)= (x + csc(x^3 +3)) ^-3

i got as far as :

f ' (x)= -3(x + csc(x^3 +3))^-4 * (1 -csc cotx(x^3 +3)) * (3x^2)

but im not sure where to go from here, do i just simplify and combine like terms?

 

[ChaoticLlama]

f(x) = (x + csc(x^3 +3)) ^-3

You pretty much have the idea, you just need to know that

dcsc(x)/dx = -csc(x)cot(x)

f'(x) = -3(x + csc(x³ + 3))^-4 * (1 - csc(x³ + 3)cot(x³ + 3) * 3x²)

f'(x) = [-3(1 - 3x²csc(x³ + 3)cot(x³ + 3)] / (x + csc(x³ + 3))^4

f'(x) = [9x²csc(x³ + 3)cot(x³ + 3) - 3] / (x + csc(x³ + 3))^4