How do you find the derivative of $cos^4(x)-sin^4(x)$ ?

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Answer 1 · 2016-06-29T15:49:13

$f^'(x)=-2sin2x$

Given
$f(x)=(cos^4x-sin^4x)$

$=>f(x)=(cos^2x-sin^2x)(cos^2x+sin^2x)$

$=>f(x)=(cos^2x-sin^2x)*1$

$=>f(x)=cos2x$

Differentiating w.r.to x using chain rule
$=>f^'(x)=d/"dx"(cos2x)=-sin(2x)d/"dx"(2x)$

$=>f^'(x)=-2sin2x$

How do you find the derivative of cos^4(x)-sin^4(x)cos^4(x)-sin^4(x)?