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Popular >

derivative of e^x(7-sqrt(x))

Solution

\frac{d}{d x} (e^{x} (7 - x))

Solution

e^{x} (7 - x) - \frac{e ^{x}}{2 x}

Solution steps

\frac{d}{d x} (e^{x} (7 - x))

Apply the Product Rule:

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

f = e^{x}, g = 7 - x

= \frac{d}{d x} (e^{x}) (7 - x) + \frac{d}{d x} (7 - x) e^{x}

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

\frac{d}{d x} (7 - x) = - \frac{1}{2 x}

= e^{x} (7 - x) + (- \frac{1}{2 x}) e^{x}

Simplify

e^{x} (7 - x) + (- \frac{1}{2 x}) e^{x} : e^{x} (7 - x) - \frac{e ^{x}}{2 x}

= e^{x} (7 - x) - \frac{e ^{x}}{2 x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^x(7-sqrt(x)) ?
The derivative of e^x(7-sqrt(x)) is e^x(7-sqrt(x))-(e^x)/(2sqrt(x))
What is the first derivative of e^x(7-sqrt(x)) ?
The first derivative of e^x(7-sqrt(x)) is e^x(7-sqrt(x))-(e^x)/(2sqrt(x))