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Popular Calculus >

derivative of 3(cos(x)^2)

Solution

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

Solution

- 3 sin (2 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 3 \cdot 2 cos (x) (- sin (x))

Simplify

3 \cdot 2 cos (x) (- sin (x)) : - 3 sin (2 x)

= - 3 sin (2 x)

Graph

Popular Examples

sum from n=1 to infinity of 1/(2^n+1)

n = 1 \sum \infty \frac{1}{2 ^{n} + 1}

derivative of 1/(e^{x^2})

\frac{d}{d x} (\frac{1}{e ^{x^{2}}})

integral of 1/(sqrt(x^2-144))

\int \frac{1}{x ^{2} - 144} d x

(\partial)/(\partial x)(2y^3-6y+x^2)

\frac{\partial}{\partial x} (2 y^{3} - 6 y + x^{2})

integral from 0 to pi/2 of xsin(x)

\int_{0}^{\frac{π}{2}} x sin (x) d x

Frequently Asked Questions (FAQ)

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