What is the derivative of (1+cos(2x)^2) ?

The derivative of (1+cos(2x)^2) is -16cos^3(x)sin(x)

What is the first derivative of (1+cos(2x)^2) ?

The first derivative of (1+cos(2x)^2) is -16cos^3(x)sin(x)

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\frac{d}{d x} ((1 + cos (2 x))^{2})

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

Solution steps

\frac{d}{d x} ((1 + cos (2 x))^{2})

Simplify

(1 + cos (2 x))^{2} : 4 cos^{4} (x)

= \frac{d}{d x} (4 cos^{4} (x))

Take the constant out:

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

= 4 \frac{d}{d x} (cos^{4} (x))

Apply the chain rule:

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

= 4 (cos (x))^{3} \frac{d}{d x} (cos (x))

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

= 4 \cdot 4 (cos (x))^{3} (- sin (x))

Simplify

= - 16 cos^{3} (x) sin (x)

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

f (x) = x^{2} + 3 x, (1, 2)

\int \frac{9 - 9 x}{1 - x} d x

y = x, at x = 4

n = 0 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

What is the derivative of (1+cos(2x)^2) ?
The derivative of (1+cos(2x)^2) is -16cos^3(x)sin(x)
What is the first derivative of (1+cos(2x)^2) ?
The first derivative of (1+cos(2x)^2) is -16cos^3(x)sin(x)