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Popular >

derivative of (x+2sqrt(x))e^x

Solution

derivative of

(x + 2 x) e^{x}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

integral of-1/(3x)

\int - \frac{1}{3 x} d x

limit as x approaches 1 of (\sqrt[3]{x+2}-1)/(x-1)

derivative of 6/5-6/5 e^{-20x}

\frac{d}{d x} (\frac{6}{5} - \frac{6}{5} e^{- 20 x})

derivative of x^2e^{-9x}

\frac{d}{d x} (x^{2} e^{- 9 x})

(\partial)/(\partial x)((100)/(x^2+y^2+3))

\frac{\partial}{\partial x} (\frac{100}{x ^{2} + y ^{2} + 3})

Frequently Asked Questions (FAQ)

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