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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

limit as x approaches 4 of ((5-x))/(x-4)

x \to 4 lim (\frac{( 5 - x )}{x - 4})

integral from-ln(4) to 0 of 4sqrt(3)e^t

\int_{- l n (4)}^{0} 43 e^{t} d t

integral from 0 to x of x^2e^{-x/4}

\int_{0}^{x} x^{2} e^{- \frac{x}{4}} d x

limit as x approaches infinity of x-e^x

x \to \infty lim (x - e^{x})

derivative of-10(sqrt(I^2+x^2)-I)derivative of

- 10 (I^{2} + x^{2} - I)

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)