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Popular Calculus >

Find the Derivative - d/dx xsin(x)

Solution

derivative of

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

Solution

sin (x) + x cos (x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = sin (x)

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

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

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

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

Simplify

= sin (x) + x cos (x)

Graph

Popular Examples

Evaluate the Integral integral of 1/(x-x^2) with respect to x

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

Find the Derivative - d/dx x/a derivative of

\frac{d}{d x} (\frac{x}{a})

Find the Derivative - d/dx 2e^(-2x)derivative of

\frac{d}{d x} (2 e^{- 2 x})

Find the Derivative - d/dy y^2 derivative of

\frac{d}{d y} (y^{2})

Find the Antiderivative -1/(e^x)integral

\frac{- 1}{( e ^{x} )}

Frequently Asked Questions (FAQ)

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