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Popular >

derivative of cos(x)sin(x)

Solution

derivative of

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)

Graph

Popular Examples

integral of 1/2 sin(2t)

\int \frac{1}{2} sin (2 t) d t

sum from n=0 to infinity of (x^n)/(n+2)

n = 0 \sum \infty \frac{x ^{n}}{n + 2}

limit as x approaches 0 of 8/(1+sin(x))

x \to 0 lim (\frac{8}{1 + sin ( x )})

derivative of (4x/(x^2+1))

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

derivative of (log_{5}(x))/(6+x^5)derivative of

\frac{lo g _{5} ( x )}{6 + x ^{5}}

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)