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Popular >

derivative of y=(sin(x))(cos(x))

Solution

derivative of

y = (sin (x)) (cos (x))

Solution

cos (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

Simplify

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

= cos (2 x)

Popular Examples

integral of e^{-2x+1}

\int e^{- 2 x + 1} d x

(\partial)/(\partial x)(-3xy(-9-x-y))

\frac{\partial}{\partial x} (- 3 x y (- 9 - x - y))

integral of 3e^{-x}

\int 3 e^{- x} d x

sum from n=1 to infinity of n^2*e^{-n^3}

n = 1 \sum \infty n^{2} \cdot e^{- n^{3}}

integral of (3x^2)/((x^3+1)^2)

\int \frac{3 x ^{2}}{( x ^{3} + 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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