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Popular Calculus >

derivative of (sin(cos(2x))^2)

Solution

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

Solution

- 4 sin (cos (2 x)) cos (cos (2 x)) sin (2 x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= - 4 sin (cos (2 x)) cos (cos (2 x)) sin (2 x)

Graph

Popular Examples

d/(dt)(sqrt(20-25sin^2(t)))

\frac{d}{d t} (20 - 25 sin^{2} (t))

integral of 3sin(sqrt(x))

\int 3 sin (x) d x

(\partial)/(\partial x)(sqrt(x^y+ln(z)))

\frac{\partial}{\partial x} (x^{y} + ln (z))

sec(x)(dy)/(dx)=e^{y+sin(x)}

sec (x) \frac{d y}{d x} = e^{y + s i n (x)}

integral of x/(x^2+7)

\int \frac{x}{x ^{2} + 7} d x

Frequently Asked Questions (FAQ)

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