What is the d/(du)(e^{vln(u)}) ?

The d/(du)(e^{vln(u)}) is vu^{v-1}

What is the first d/(du)(e^{vln(u)}) ?

The first d/(du)(e^{vln(u)}) is vu^{v-1}

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\frac{d}{d u} (e^{v l n (u)})

v u^{v - 1}

Solution steps

\frac{d}{d u} (e^{v l n (u)})

Simplify

e^{v l n (u)} : u^{v}

= \frac{d}{d u} (u^{v})

Treat

v

as a constant

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= v u^{v - 1}

(4 x) (2 x^{2})

(2^{2} 0.3)^{4} \cdot (2.3)^{- 2}

e^{- l n (x y)}

(x - 2)^{2} (2 x + 3)^{2}