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Popular >

derivative of sqrt(xe^{2x)}

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of sin^2(pi/4+t/2)

\int sin^{2} (\frac{π}{4} + \frac{t}{2}) d t

limit as x approaches-7 of x^2-49

x \to - 7 lim (x^{2} - 49)

derivative of 1/(t^2+5t-1)derivative of

\frac{1}{t ^{2} + 5 t - 1}

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

y = \frac{4 x}{x ^{2} + 1}, (- 1, - 2)

area x^3-13x^2+30x,-x^3+13x^2-30x area

x^{3} - 13 x^{2} + 30 x, - x^{3} + 13 x^{2} - 30 x

Frequently Asked Questions (FAQ)

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