What is the derivative of (1+cos^2(x))^4 ?

The derivative of (1+cos^2(x))^4 is -4sin(2x)(1+cos^2(x))^3

What is the first derivative of (1+cos^2(x))^4 ?

The first derivative of (1+cos^2(x))^4 is -4sin(2x)(1+cos^2(x))^3

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derivative of

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

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

Solution steps

\frac{d}{d x} ((1 + cos^{2} (x))^{4})

Apply the chain rule:

4 (1 + cos^{2} (x))^{3} \frac{d}{d x} (1 + cos^{2} (x))

= 4 (1 + cos^{2} (x))^{3} \frac{d}{d x} (1 + cos^{2} (x))

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

= 4 (1 + cos^{2} (x))^{3} (- sin (2 x))

Simplify

= - 4 sin (2 x) (1 + cos^{2} (x))^{3}

y = x^{3} - 16 x^{2} + 45 x + 6

\int 4 sin (x) + 4 d x

\frac{d y}{d x} = \frac{1}{4} y

x \to - 5 - lim (\frac{6}{x ^{2} - 25})

f (x) = sin (x^{2} + 2)

What is the derivative of (1+cos^2(x))^4 ?
The derivative of (1+cos^2(x))^4 is -4sin(2x)(1+cos^2(x))^3
What is the first derivative of (1+cos^2(x))^4 ?
The first derivative of (1+cos^2(x))^4 is -4sin(2x)(1+cos^2(x))^3