What is the derivative of cos^2(3sqrt(x)) ?

The derivative of cos^2(3sqrt(x)) is -(3cos(3sqrt(x))sin(3sqrt(x)))/(sqrt(x))

What is the first derivative of cos^2(3sqrt(x)) ?

The first derivative of cos^2(3sqrt(x)) is -(3cos(3sqrt(x))sin(3sqrt(x)))/(sqrt(x))

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\frac{d}{d x} (cos^{2} (3 x))

- \frac{3 cos ( 3 x ) sin ( 3 x )}{x}

Solution steps

\frac{d}{d x} (cos^{2} (3 x))

Apply the chain rule:

2 cos (3 x) \frac{d}{d x} (cos (3 x))

= 2 cos (3 x) \frac{d}{d x} (cos (3 x))

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \frac{3}{2 x}

= 2 cos (3 x) (- sin (3 x) \frac{3}{2 x})

Simplify

2 cos (3 x) (- sin (3 x) \frac{3}{2 x}) : - \frac{3 cos ( 3 x ) sin ( 3 x )}{x}

= - \frac{3 cos ( 3 x ) sin ( 3 x )}{x}

What is the derivative of cos^2(3sqrt(x)) ?
The derivative of cos^2(3sqrt(x)) is -(3cos(3sqrt(x))sin(3sqrt(x)))/(sqrt(x))
What is the first derivative of cos^2(3sqrt(x)) ?
The first derivative of cos^2(3sqrt(x)) is -(3cos(3sqrt(x))sin(3sqrt(x)))/(sqrt(x))