What is the derivative of (1+cos^2(x))^3 ?

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

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

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

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derivative of

(1 + cos^{2} (x))^{3}

- 3 sin (2 x) (1 + cos^{2} (x))^{2}

Solution steps

\frac{d}{d x} ((1 + cos^{2} (x))^{3})

Apply the chain rule:

3 (1 + cos^{2} (x))^{2} \frac{d}{d x} (1 + cos^{2} (x))

= 3 (1 + cos^{2} (x))^{2} \frac{d}{d x} (1 + cos^{2} (x))

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

= 3 (1 + cos^{2} (x))^{2} (- sin (2 x))

Simplify

= - 3 sin (2 x) (1 + cos^{2} (x))^{2}

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

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

\frac{d}{d x} (\frac{16}{x ^{2}})

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

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

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