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Popular >

derivative of (xcos(x)sin(x))

Solution

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

Solution

cos (x) sin (x) + x cos (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (x) sin (x)) = cos (2 x)

= 1 \cdot cos (x) sin (x) + cos (2 x) x

Simplify

= cos (x) sin (x) + x cos (2 x)

Popular Examples

(\partial)/(\partial x)(e^{2(2x+y)})

\frac{\partial}{\partial x} (e^{2 (2 x + y)})

derivative of ln(x^2-1)derivative of

ln (x^{2} - 1)

sum from n=0 to infinity of nx^{n-1}

n = 0 \sum \infty n x^{n - 1}

derivative of x^{(-5/9})

\frac{d}{d x} (x^{\frac{- 5}{9}})

derivative of f(x)=e^{-(x^2)/2}derivative of

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

Frequently Asked Questions (FAQ)

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