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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 3 cos ^{3} ( x )} \frac{d}{d x} (3 cos^{3} (x))

= \frac{1}{2 3 cos ^{3} ( x )} \frac{d}{d x} (3 cos^{3} (x))

\frac{d}{d x} (3 cos^{3} (x)) = - 9 cos^{2} (x) sin (x)

= \frac{1}{2 3 cos ^{3} ( x )} (- 9 cos^{2} (x) sin (x))

Simplify

\frac{1}{2 3 cos ^{3} ( x )} (- 9 cos^{2} (x) sin (x)) : - \frac{3 3 sin ( x ) cos ( x )}{2}

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

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