What is the derivative of (9e^{2w}+e^w)/(e^w) ?

The derivative of (9e^{2w}+e^w)/(e^w) is 9e^w

What is the first derivative of (9e^{2w}+e^w)/(e^w) ?

The first derivative of (9e^{2w}+e^w)/(e^w) is 9e^w

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derivative of

\frac{9 e ^{2 w} + e ^{w}}{e ^{w}}

9 e^{w}

Solution steps

\frac{d}{d w} (\frac{9 e ^{2 w} + e ^{w}}{e ^{w}})

Simplify

\frac{9 e ^{2 w} + e ^{w}}{e ^{w}} : 9 e^{w} + 1

= \frac{d}{d w} (9 e^{w} + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d w} (9 e^{w}) + \frac{d}{d w} (1)

\frac{d}{d w} (9 e^{w}) = 9 e^{w}

\frac{d}{d w} (1) = 0

= 9 e^{w} + 0

Simplify

= 9 e^{w}

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\int_{- \infty}^{12} r e^{\frac{r}{4}} d r

What is the derivative of (9e^{2w}+e^w)/(e^w) ?
The derivative of (9e^{2w}+e^w)/(e^w) is 9e^w
What is the first derivative of (9e^{2w}+e^w)/(e^w) ?
The first derivative of (9e^{2w}+e^w)/(e^w) is 9e^w