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Popular >

d/(dy)(e^yy^e)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e e^{y} = e^{1 + y}

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

Popular Examples

integral of 4e^xcos(2x)

\int 4 e^{x} cos (2 x) d x

tangent of f(x)=(1+3x)(5-2x),\at x=2 tangent of

f (x) = (1 + 3 x) (5 - 2 x), at x = 2

inverse oflaplace s/((s+1)(s^2+4))inverse laplace

\frac{s}{( s + 1 ) ( s ^{2} + 4 )}

(d^2)/(dx^2)(1/(x^{10)})

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{10}})

integral of-tan(t)

\int - tan (t) d t

Frequently Asked Questions (FAQ)

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