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Popular Calculus >

derivative of 9cos^3(x)

Solution

\frac{d}{d x} (9 cos^{3} (x))

Solution

- 27 cos^{2} (x) sin (x)

Solution steps

\frac{d}{d x} (9 cos^{3} (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= - 27 cos^{2} (x) sin (x)

Graph

Popular Examples

integral of 3/(xln(2x))

\int \frac{3}{x ln ( 2 x )} d x

integral of (20x^3-40x^2+7)/(x^2-2x)

\int \frac{20 x ^{3} - 40 x ^{2} + 7}{x ^{2} - 2 x} d x

integral of cos(ln(5x))

\int cos (ln (5 x)) d x

integral of 4/15 x^{5/2}+9cos(x)+Cx+C

\int \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C x + C d x

integral of 1/(x^2)+1/x

\int \frac{1}{x ^{2}} + \frac{1}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 9cos^3(x) ?
The derivative of 9cos^3(x) is -27cos^2(x)sin(x)
What is the first derivative of 9cos^3(x) ?
The first derivative of 9cos^3(x) is -27cos^2(x)sin(x)