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Popular >

derivative of 2cos^2(2x)

Solution

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

Solution

- 4 sin (4 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

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

Simplify

2 \cdot 2 cos (2 x) (- sin (2 x) \cdot 2) : - 4 sin (4 x)

= - 4 sin (4 x)

Popular Examples

limit as x approaches 3-of (3x+2)/(x-3)

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

tangent of f(x)= 1/(3-2x),\at x=-1 tangent of

f (x) = \frac{1}{3 - 2 x}, at x = - 1

(\partial)/(\partial x)(3/(3x+y))

\frac{\partial}{\partial x} (\frac{3}{3 x + y})

integral of-1/2 y

\int - \frac{1}{2} y d y

limit as x approaches-1 of x+3

x \to - 1 lim (x + 3)

Frequently Asked Questions (FAQ)

What is the derivative of 2cos^2(2x) ?
The derivative of 2cos^2(2x) is -4sin(4x)
What is the first derivative of 2cos^2(2x) ?
The first derivative of 2cos^2(2x) is -4sin(4x)