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Popular Calculus >

derivative of sqrt(w)e^{7w}

Solution

derivative of

w e^{7 w}

Solution

\frac{e ^{7 w}}{2 w} + 7 e^{7 w} w

Solution steps

\frac{d}{d w} (w e^{7 w})

Apply the Product Rule:

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

f = w, g = e^{7 w}

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

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

\frac{d}{d w} (e^{7 w}) = e^{7 w} \cdot 7

= \frac{1}{2 w} e^{7 w} + e^{7 w} \cdot 7 w

\frac{1}{2 w} e^{7 w} = \frac{e ^{7 w}}{2 w}

= \frac{e ^{7 w}}{2 w} + 7 e^{7 w} w

Graph

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d er i v a t i v e f (x) = x^{- 15}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(w)e^{7w} ?
The derivative of sqrt(w)e^{7w} is (e^{7w})/(2sqrt(w))+7e^{7w}sqrt(w)
What is the first derivative of sqrt(w)e^{7w} ?
The first derivative of sqrt(w)e^{7w} is (e^{7w})/(2sqrt(w))+7e^{7w}sqrt(w)