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Popular >

derivative of 10cos^3(x)

Solution

\frac{d}{d x} (10 cos^{3} (x))

Solution

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

Solution steps

\frac{d}{d x} (10 cos^{3} (x))

Take the constant out:

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

= 10 \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)

= 10 \cdot 3 (cos (x))^{2} (- sin (x))

Simplify

= - 30 cos^{2} (x) sin (x)

Graph

Popular Examples

derivative of f(x)=sin(x)+3/4 cot(x)derivative of

f (x) = sin (x) + \frac{3}{4} cot (x)

derivative of 1/(x^{-9)}derivative of

\frac{1}{x ^{- 9}}

derivative of (1+7/x ^5)

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

derivative of y=ln(sqrt(x^2-9))derivative of

y = ln (x^{2} - 9)

limit as x approaches-3 of sqrt(5x^2+2x)

x \to - 3 lim (5 x^{2} + 2 x)

Frequently Asked Questions (FAQ)

What is the derivative of 10cos^3(x) ?
The derivative of 10cos^3(x) is -30cos^2(x)sin(x)
What is the first derivative of 10cos^3(x) ?
The first derivative of 10cos^3(x) is -30cos^2(x)sin(x)