What is expand e^{5t}((dv)/(dt)+5v) ?

The solution to expand e^{5t}((dv)/(dt)+5v) is e^{5t}(dv)/(dt)+5e^{5t}v

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expand e^{5t}((dv)/(dt)+5v)

expand

e^{5 t} (\frac{d v}{d t} + 5 v)

e^{5 t} \frac{d v}{d t} + 5 e^{5 t} v

Solution steps

e^{5 t} (\frac{d v}{d t} + 5 v)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{5 t}, b = \frac{d v}{d t}, c = 5 v

= e^{5 t} \frac{d v}{d t} + e^{5 t} \cdot 5 v

= e^{5 t} \frac{d v}{d t} + 5 e^{5 t} v

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What is expand e^{5t}((dv)/(dt)+5v) ?
The solution to expand e^{5t}((dv)/(dt)+5v) is e^{5t}(dv)/(dt)+5e^{5t}v