Question #36066

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Question #36066

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Answer 1 · 2017-06-06T00:15:31

Let's use the product rule:

$\frac{d ((x + 1) (e^{x}))}{d x} = \frac{d (x + 1)}{d x} (e^{x}) + (x + 1) \frac{d (e^{x})}{d x}$ $(d((x+1)(e^x)))/dx = (d(x+1))/dx(e^x)+ (x+1)(d(e^x))/dx$

$\frac{d ((x + 1) e^{x})}{d x} = (1) (e^{x}) + (x + 1) (e^{x})$ $(d((x+1)e^x))/dx = (1)(e^x)+ (x+1)(e^x)$

$\frac{d ((x + 1) e^{x})}{d x} = (x + 2) (e^{x})$ $(d((x+1)e^x))/dx = (x+2)(e^x)$

Answer 2 · 2017-06-06T00:20:05

$\frac{d y}{d y} = e^{x} (x + 2)$ $dy/dy=e^x(x+2)$

Explanation:

$\frac{d y}{d y} = \frac{d}{d x} (x + 1) e^{x}$ $dy/dy=d/dx(x+1)e^x$

$\frac{d y}{d x} = (x + 1) \frac{d}{d x} (e^{x}) + e^{x} \frac{d}{d x} (x + 1)$ $dy/dx=(x+1)d/dx(e^x)+e^xd/dx(x+1)$

$\frac{d y}{d x} = (x + 1) e^{x} + e^{x}$ $dy/dx=(x+1)e^x+e^x$

$\frac{d y}{d y} = e^{x} (x + 2)$ $dy/dy=e^x(x+2)$

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Question #36066

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