What is the derivative of cos(xcos(x)) ?

The derivative of cos(xcos(x)) is -sin(2x)

What is the first derivative of cos(xcos(x)) ?

The first derivative of cos(xcos(x)) is -sin(2x)

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\frac{d}{d x} (cos (x) cos (x))

- sin (2 x)

Solution steps

\frac{d}{d x} (cos (x) cos (x))

Simplify

cos (x) cos (x) : cos^{2} (x)

= \frac{d}{d x} (cos^{2} (x))

Apply the chain rule:

2 cos (x) \frac{d}{d x} (cos (x))

= 2 cos (x) \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= 2 cos (x) (- sin (x))

Simplify

2 cos (x) (- sin (x)) : - sin (2 x)

= - sin (2 x)

\frac{d}{d x} (\frac{x + 8}{3 x ^{2} e ^{x}})

\frac{d}{d x} (- \frac{x ^{2}}{2} + 5 x + 3)

y^{^{'}} = \frac{( x ^{2} )}{y ( 1 + x ^{3} )}

\int_{0}^{x} e^{- t} d t

\frac{d}{d x} ((x - x^{3})^{x})

What is the derivative of cos(xcos(x)) ?
The derivative of cos(xcos(x)) is -sin(2x)
What is the first derivative of cos(xcos(x)) ?
The first derivative of cos(xcos(x)) is -sin(2x)