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))

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العربية

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

- \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}

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))