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Popular >

derivative of (1+cos^2(x)^6)

Solution

\frac{d}{d x} ((1 + cos^{2} (x))^{6})

Solution

- 6 sin (2 x) (1 + cos^{2} (x))^{5}

Solution steps

\frac{d}{d x} ((1 + cos^{2} (x))^{6})

Apply the chain rule:

6 (1 + cos^{2} (x))^{5} \frac{d}{d x} (1 + cos^{2} (x))

= 6 (1 + cos^{2} (x))^{5} \frac{d}{d x} (1 + cos^{2} (x))

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

= 6 (1 + cos^{2} (x))^{5} (- sin (2 x))

Simplify

= - 6 sin (2 x) (1 + cos^{2} (x))^{5}

Popular Examples

\frac{d}{d t} (15 t^{2})

derivative of x^8-x^{1/2}derivative of

x^{8} - x^{\frac{1}{2}}

integral of (10x^2-9x+16)/(x^3+4x)

\int \frac{10 x ^{2} - 9 x + 16}{x ^{3} + 4 x} d x

-3y^'+(3y)/x =x^3y^4

- 3 y^{^{'}} + \frac{3 y}{x} = x^{3} y^{4}

(dy)/(dt)=2y+y^3,y(0)=1

\frac{d y}{d t} = 2 y + y^{3}, y (0) = 1

Frequently Asked Questions (FAQ)

What is the derivative of (1+cos^2(x)^6) ?
The derivative of (1+cos^2(x)^6) is -6sin(2x)(1+cos^2(x))^5
What is the first derivative of (1+cos^2(x)^6) ?
The first derivative of (1+cos^2(x)^6) is -6sin(2x)(1+cos^2(x))^5