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Popular >

derivative of sqrt(x)e^{2x}

Solution

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

Solution

\frac{e ^{2 x}}{2 x} + 2 e^{2 x} x

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{2 x}

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

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

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

= \frac{1}{2 x} e^{2 x} + e^{2 x} \cdot 2 x

\frac{1}{2 x} e^{2 x} = \frac{e ^{2 x}}{2 x}

= \frac{e ^{2 x}}{2 x} + 2 e^{2 x} x

Popular Examples

limit as x approaches infinity of a^{-x}

x \to \infty lim (a^{- x})

(\partial}{\partial x}(\frac{3x+y)/z)

\frac{\partial}{\partial x} (\frac{3 x + y}{z})

derivative of 11xarcsin(x)

\frac{d}{d x} (11 x arcsin (x))

(dy)/(dx)=(y^3)/(e^x)

\frac{d y}{d x} = \frac{y ^{3}}{e ^{x}}

(\partial)/(\partial x)(sec(x/2))

\frac{\partial}{\partial x} (sec (\frac{x}{2}))

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)e^{2x} ?
The derivative of sqrt(x)e^{2x} is (e^{2x})/(2sqrt(x))+2e^{2x}sqrt(x)
What is the first derivative of sqrt(x)e^{2x} ?
The first derivative of sqrt(x)e^{2x} is (e^{2x})/(2sqrt(x))+2e^{2x}sqrt(x)