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Popular >

derivative of cos(x(sin(x)))

Solution

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

Solution

cos (2 x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = sin (x)

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

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

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

= (- sin (x)) sin (x) + cos (x) cos (x)

Simplify

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

Popular Examples

integral from 0 to pi/(12) of cos(6x)

\int_{0}^{\frac{π}{12}} cos (6 x) d x

integral from 0 to 2 of x3^x

\int_{0}^{2} x 3^{x} d x

integral of ((x^2+2))/(x+2)

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

(\partial)/(\partial x)(((x-y))/(ln(x/y)))

\frac{\partial}{\partial x} \frac{( x - y )}{ln ( \frac{x}{y} )}

2(d^2y)/(dx^2)-20(dy)/(dx)+48y=3sin(5x)

2 \frac{d ^{2} y}{d x ^{2}} - 20 \frac{d y}{d x} + 48 y = 3 sin (5 x)

Frequently Asked Questions (FAQ)

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