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Popular >

derivative of y=2xsin(x)+x^2e^x

Solution

derivative of

y = 2 x sin (x) + x^{2} e^{x}

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

derivative of-2x^2-5x+2

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

integral of 1/(sqrt(x^2-81))

\int \frac{1}{x ^{2} - 81} d x

y^'=-(3y)/t-2-t^{-4},y(1)=4

y^{^{'}} = - \frac{3 y}{t} - 2 - t^{- 4}, y (1) = 4

(\partial)/(\partial y)((x-3)/(y^2+1))

\frac{\partial}{\partial y} (\frac{x - 3}{y ^{2} + 1})

limit as x approaches-infinity of x-5

x \to - \infty lim (x - 5)

Frequently Asked Questions (FAQ)

What is the derivative of y=2xsin(x)+x^2e^x ?
The derivative of y=2xsin(x)+x^2e^x is 2(sin(x)+xcos(x))+2xe^x+e^xx^2
What is the first derivative of y=2xsin(x)+x^2e^x ?
The first derivative of y=2xsin(x)+x^2e^x is 2(sin(x)+xcos(x))+2xe^x+e^xx^2