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Popular >

derivative of sqrt(x^2+1)+2xe^x

Solution

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

Solution

\frac{x}{x ^{2} + 1} + 2 (e^{x} + e^{x} x)

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{2} + 1) + \frac{d}{d x} (2 x e^{x})

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

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

= \frac{x}{x ^{2} + 1} + 2 (e^{x} + e^{x} x)

Graph

Popular Examples

(\partial)/(\partial x)(7e^{x/y})

\frac{\partial}{\partial x} (7 e^{\frac{x}{y}})

integral of (x^2sin(3x))

\int (x^{2} sin (3 x)) d x

integral of 1/(x^2sqrt(1-\frac{1){x^2)}}

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

tangent of y^2=5x^4-x^2,(1,2)tangent of

y^{2} = 5 x^{4} - x^{2}, (1, 2)

limit as x approaches 0 of (e^x-1)/(12x)

x \to 0 lim (\frac{e ^{x} - 1}{12 x})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2+1)+2xe^x ?
The derivative of sqrt(x^2+1)+2xe^x is x/(sqrt(x^2+1))+2(e^x+e^xx)
What is the first derivative of sqrt(x^2+1)+2xe^x ?
The first derivative of sqrt(x^2+1)+2xe^x is x/(sqrt(x^2+1))+2(e^x+e^xx)