find the derivative of f(x) =4/x^5+cosx

Question

how do i solve this question on a math test that i have tomorrow?

Answer 1

Remember the formulae d /dx (cos x) = - sinx

d/dx ( x ⁿ ) = n x ^n-1

f(x) = (4/x ⁵)+ Cosx.

Apply derivative on each side with respect of x.

f'(x) = d/dx[(4 / x ⁵)+ Cos x]

= d/dx  (4/x ⁵) + d/dx (Cos x)

= 4 d/dx  (1/x⁴) - sinx

= 4 d/dx  ( x^-5) - sinx

= 4 * - 5 ( x^-5-1) - sinx

= - 20 x^{- 6} - sinx

= (- 20/x⁶ ) - sinx

f'(x) = (- 20/x⁶) - sinx.