What is expand e^y((dy)/(dx)+1) ?

The solution to expand e^y((dy)/(dx)+1) is e^y(dy)/(dx)+e^y

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expand e^y((dy)/(dx)+1)

expand

e^{y} (\frac{d y}{d x} + 1)

e^{y} \frac{d y}{d x} + e^{y}

Solution steps

e^{y} (\frac{d y}{d x} + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{y}, b = \frac{d y}{d x}, c = 1

= e^{y} \frac{d y}{d x} + e^{y} \cdot 1

= e^{y} \frac{d y}{d x} + 1 \cdot e^{y}

Multiply:

1 \cdot e^{y} = e^{y}

= e^{y} \frac{d y}{d x} + e^{y}

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a x^{2} + (a + b) x - c

(3 - \frac{e ^{x}}{10})^{2}

What is expand e^y((dy)/(dx)+1) ?
The solution to expand e^y((dy)/(dx)+1) is e^y(dy)/(dx)+e^y