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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)

Graph

Popular Examples

integral of (1/x-5x)

\int (\frac{1}{x} - 5 x) d x

t(dy)/(dt)+(t+1)y=t

t \frac{d y}{d t} + (t + 1) y = t

derivative of x^6-4x^5+5x^4-5x^2+4x-1

\frac{d}{d x} (x^{6} - 4 x^{5} + 5 x^{4} - 5 x^{2} + 4 x - 1)

integral from 1 to 5 of 4r^2ln(r)

\int_{1}^{5} 4 r^{2} ln (r) d r

derivative of f(x)= x/(x^2-x)derivative of

f (x) = \frac{x}{x ^{2} - 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)