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

The derivative of y=cos^3(x) is -3cos^2(x)sin(x)

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

The first derivative of y=cos^3(x) is -3cos^2(x)sin(x)

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derivative of

y = cos^{3} (x)

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

Solution steps

\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)

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

Simplify

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

\int_{0}^{\infty} \frac{1}{x ^{3}} d x

\int (x^{4} + 6 x^{2}) (4 x^{3} + 12 x) d x

\frac{d}{d x} (e^{x} (x - 2))

\frac{30}{x ^{7}}

x \to 0 + lim ((1 + x)^{\frac{3}{x}})

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