What is the derivative of $f (x) = {cos}^{4} (2 x)$ $f(x)=cos^4(2x)$ ?

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Answer 1 · 2015-11-09T18:46:06

$- 8 {cos}^{3} (2 x) sin (2 x)$ $-8cos^3(2x)sin(2x)$

$f (x) = {(cos (2 x))}^{4}$ $f(x) = (cos(2x))^4$

$f'(x) = 4(cos(2x))^3 d/dx(cos(2x))$ (chain rule)

$= 4(cos(2x))^3 (-sin(2x) d/dx(2x))$

$= 4(cos(2x))^3 (-sin(2x) (2))$

$= -8cos^3(2x)sin(2x)$

What is the derivative of f(x)=cos^4(2x)f(x)=cos4(2x)f(x)=cos^4(2x)?