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

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

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expand e^{x+y}(1+(dy)/(dx))

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Multiply:

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

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

(vx + v x^{3}) (v d x + x d v)

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\frac{2 ( 7 - 13 )}{3}

3 (2 - e^{\frac{1}{5}})

(5 - 3 x)^{3} d x

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