find the derivative using the chain rule

Question

let f(x)=(((x+x^7)^4)+(sin(x)))^4

f'(x)=?

Answer 1

Take the derivative of the outside function f(x) = w⁴ where "w' is u⁴ + sin(x) and u = x + x⁷.

Then f '(x) = 4w³•w'

Now determine w', again using the chain rule. w' = 4u³•u' + cos(x)

Now determine u' using the power rule. u' = 1 + 7x⁶ which makes w' = 4(x + x⁷)³•(1 + 7x⁶) + cos(x).

That makes f '(x) = 4((x + x⁷)⁴ + sin(x))³•(4(x + x⁷)³•(1 + 7x⁶) + cos(x))