What is the derivative of x^5e^{-3ln(x}) ?

The derivative of x^5e^{-3ln(x}) is 2x

What is the first derivative of x^5e^{-3ln(x}) ?

The first derivative of x^5e^{-3ln(x}) is 2x

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\frac{d}{d x} (x^{5} e^{- 3 l n (x)})

2 x

Solution steps

\frac{d}{d x} (x^{5} e^{- 3 l n (x)})

Simplify

x^{5} e^{- 3 l n (x)} : x^{2}

= \frac{d}{d x} (x^{2})

Apply the Power Rule:

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

= 2 x^{2 - 1}

Simplify

= 2 x

What is the derivative of x^5e^{-3ln(x}) ?
The derivative of x^5e^{-3ln(x}) is 2x
What is the first derivative of x^5e^{-3ln(x}) ?
The first derivative of x^5e^{-3ln(x}) is 2x