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Popular >

derivative of e^{2x}+2xe^{2x}

Solution

derivative of

e^{2 x} + 2 x e^{2 x}

Solution

4 e^{2 x} + 4 e^{2 x} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{2 x} \cdot 2 + 2 (e^{2 x} + 2 e^{2 x} x)

Simplify

e^{2 x} \cdot 2 + 2 (e^{2 x} + 2 e^{2 x} x) : 4 e^{2 x} + 4 e^{2 x} x

= 4 e^{2 x} + 4 e^{2 x} x

Popular Examples

derivative of cos((1-e^{5x}/(1+e^{5x)}))

\frac{d}{d x} (cos (\frac{1 - e ^{5 x}}{1 + e ^{5 x}}))

integral of 1/(6x^2)

\int \frac{1}{6 x ^{2}} d x

(\partial)/(\partial x)(2sqrt(x)+4y)

\frac{\partial}{\partial x} (2 x + 4 y)

y^'-(2y)/x =x^2

y^{^{'}} - \frac{2 y}{x} = x^{2}

area y=7e^x,y=7e^{-x},x=1 area

y = 7 e^{x}, y = 7 e^{- x}, x = 1

Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}+2xe^{2x} ?
The derivative of e^{2x}+2xe^{2x} is 4e^{2x}+4e^{2x}x
What is the first derivative of e^{2x}+2xe^{2x} ?
The first derivative of e^{2x}+2xe^{2x} is 4e^{2x}+4e^{2x}x