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Popular >

derivative of sqrt(x)e^x

Solution

derivative of

x e^{x}

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

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

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

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

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

Graph

Popular Examples

derivative of e^{x^2*\sqrt[3]{4x-1}}

\frac{d}{d x} (e^{x^{2} \cdot 3 4 x - 1})

integral of (2x+1)/(2x)

\int \frac{2 x + 1}{2 x} d x

integral of (6x^4-5x^3+4x^2)/(2x^2-x+1)

\int \frac{6 x ^{4} - 5 x ^{3} + 4 x ^{2}}{2 x ^{2} - x + 1} d x

integral of (5x^3-3\sqrt[5]{x})/(5x)

\int \frac{5 x ^{3} - 3 5 x}{5 x} d x

tangent of g(x)=2-x^3 tangent of

g (x) = 2 - x^{3}

Frequently Asked Questions (FAQ)

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