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Popular >

derivative of e^yy^e

Solution

derivative of

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}

Graph

Popular Examples

(\partial)/(\partial x)(7^{x^4+2x})

\frac{\partial}{\partial x} (7^{x^{4} + 2 x})

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\int cos (θ) (tan (θ) + sec (θ)) d θ

(\partial)/(\partial x)(x^5e^{xy})

\frac{\partial}{\partial x} (x^{5} e^{x y})

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d/(dy)(x^2(y-x))

\frac{d}{d y} (x^{2} (y - x))

Frequently Asked Questions (FAQ)

What is the derivative of e^yy^e ?
The derivative of e^yy^e is e^yy^e+e^{1+y}y^{e-1}
What is the first derivative of e^yy^e ?
The first derivative of e^yy^e is e^yy^e+e^{1+y}y^{e-1}