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Popular >

derivative of f(x)=3cos^2(x)

Solution

derivative of

f (x) = 3 cos^{2} (x)

Solution

- 3 sin (2 x)

Solution steps

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

Take the constant out:

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

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

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)

Popular Examples

integral of 5cos(pix-3)

\int 5 cos (π x - 3) d x

derivative of (4x)/(sqrt(x^2+2))derivative of

\frac{4 x}{x ^{2} + 2}

(\partial)/(\partial x)(x(10-x-y))

\frac{\partial}{\partial x} (x (10 - x - y))

(d^2y)/(dx^2)-4(dy)/(dx)=12cos(2x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} = 12 cos (2 x)

integral of (6-6x)/(1-sqrt(x))

\int \frac{6 - 6 x}{1 - x} d x

Frequently Asked Questions (FAQ)

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