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Popular >

d/(dy)((x)(e^x+x^e))

Solution

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

Solution

e^{y} + y^{e} + y (e^{y} + e y^{e - 1})

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{y} + y^{e}

= \frac{d y}{d y} (e^{y} + y^{e}) + \frac{d}{d y} (e^{y} + y^{e}) y

\frac{d y}{d y} = 1

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

= 1 \cdot (e^{y} + y^{e}) + (e^{y} + e y^{e - 1}) y

Simplify

= e^{y} + y^{e} + y (e^{y} + e y^{e - 1})

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Frequently Asked Questions (FAQ)

What is the d/(dy)((x)(e^x+x^e)) ?
The d/(dy)((x)(e^x+x^e)) is e^y+y^e+y(e^y+ey^{e-1})
What is the first d/(dy)((x)(e^x+x^e)) ?
The first d/(dy)((x)(e^x+x^e)) is e^y+y^e+y(e^y+ey^{e-1})