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Popular >

derivative of cos^2(sqrt(x))

Solution

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

Solution

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

Solution steps

\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)) = - \frac{sin ( x )}{2 x}

= 2 cos (x) (- \frac{sin ( x )}{2 x})

Simplify

2 cos (x) (- \frac{sin ( x )}{2 x}) : - \frac{sin ( x ) cos ( x )}{x}

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

Graph

Popular Examples

integral of 21sin^2(x)cos^2(x)

\int 21 sin^{2} (x) cos^{2} (x) d x

integral of (x+23)/(x^2+20x+104)

\int \frac{x + 23}{x ^{2} + 20 x + 104} d x

integral of 6xln(2x)

\int 6 x ln (2 x) d x

integral from 0 to 2pi of xe^{-ix}

\int_{0}^{2 π} x e^{- i x} d x

integral of x*cos(x)-x*sin(x)

\int x \cdot cos (x) - x \cdot sin (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of cos^2(sqrt(x)) ?
The derivative of cos^2(sqrt(x)) is -(sin(sqrt(x))cos(sqrt(x)))/(sqrt(x))
What is the first derivative of cos^2(sqrt(x)) ?
The first derivative of cos^2(sqrt(x)) is -(sin(sqrt(x))cos(sqrt(x)))/(sqrt(x))