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Popular >

derivative of xcos(x+x^2sin(x))

Solution

\frac{d}{d x} (x cos (x) + x^{2} sin (x))

Solution

cos (x) + x sin (x) + x^{2} cos (x)

Solution steps

\frac{d}{d x} (x cos (x) + x^{2} sin (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= cos (x) - x sin (x) + 2 x sin (x) + cos (x) x^{2}

Simplify

= cos (x) + x sin (x) + x^{2} cos (x)

Graph

Popular Examples

derivative of f(x)=533.33+(x/(250))^2 derivative of

f (x) = 533.33 + (\frac{x}{250})^{2}

integral of 3x+1

\int 3 x + 1 d x

integral from 0 to 1 of xe^{1-x^2}

\int_{0}^{1} x e^{1 - x^{2}} d x

(3sqrt(x-1)+4sqrt(5-x))^'

(3 x - 1 + 4 5 - x)^{^{'}}

integral of 1/(5x)

\int \frac{1}{5 x} d x

Frequently Asked Questions (FAQ)

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