What is the derivative of 5cos^3(x) ?

The derivative of 5cos^3(x) is -15cos^2(x)sin(x)

What is the first derivative of 5cos^3(x) ?

The first derivative of 5cos^3(x) is -15cos^2(x)sin(x)

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\frac{d}{d x} (5 cos^{3} (x))

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

Solution steps

\frac{d}{d x} (5 cos^{3} (x))

Take the constant out:

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

= 5 \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)

= 5 \cdot 3 (cos (x))^{2} (- sin (x))

Simplify

= - 15 cos^{2} (x) sin (x)

\int \frac{x ^{2} + x + 3}{x ^{4} + 6 x ^{2} + 9} d x

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

f (x) = \frac{e ^{x}}{x}, (1, e)

\frac{d}{d x} (\frac{x ^{2} - 6 x + 5}{x ^{2} + 7})

\int_{0}^{3} (3 x^{2} + x - 2) d x

What is the derivative of 5cos^3(x) ?
The derivative of 5cos^3(x) is -15cos^2(x)sin(x)
What is the first derivative of 5cos^3(x) ?
The first derivative of 5cos^3(x) is -15cos^2(x)sin(x)