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Popular Calculus >

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

Solution

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

Graph

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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))