What is the derivative of 4cos^3(x-3cos(x)) ?

The derivative of 4cos^3(x-3cos(x)) is 12sin^3(x)-9sin(x)

What is the first derivative of 4cos^3(x-3cos(x)) ?

The first derivative of 4cos^3(x-3cos(x)) is 12sin^3(x)-9sin(x)

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\frac{d}{d x} (4 cos^{3} (x) - 3 cos (x))

12 sin^{3} (x) - 9 sin (x)

Solution steps

\frac{d}{d x} (4 cos^{3} (x) - 3 cos (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 cos^{3} (x)) - \frac{d}{d x} (3 cos (x))

\frac{d}{d x} (4 cos^{3} (x)) = - 12 cos^{2} (x) sin (x)

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

= - 12 cos^{2} (x) sin (x) - (- 3 sin (x))

Simplify

- 12 cos^{2} (x) sin (x) - (- 3 sin (x)) : 12 sin^{3} (x) - 9 sin (x)

= 12 sin^{3} (x) - 9 sin (x)

What is the derivative of 4cos^3(x-3cos(x)) ?
The derivative of 4cos^3(x-3cos(x)) is 12sin^3(x)-9sin(x)
What is the first derivative of 4cos^3(x-3cos(x)) ?
The first derivative of 4cos^3(x-3cos(x)) is 12sin^3(x)-9sin(x)