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

The derivative of e^{3ln(x^2}) is 6x^5

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

The first derivative of e^{3ln(x^2}) is 6x^5

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\frac{d}{d x} (e^{3 l n (x^{2})})

6 x^{5}

Solution steps

\frac{d}{d x} (e^{3 l n (x^{2})})

Simplify

e^{3 l n (x^{2})} : x^{6}

= \frac{d}{d x} (x^{6})

Apply the Power Rule:

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

= 6 x^{6 - 1}

Simplify

= 6 x^{5}

What is the derivative of e^{3ln(x^2}) ?
The derivative of e^{3ln(x^2}) is 6x^5
What is the first derivative of e^{3ln(x^2}) ?
The first derivative of e^{3ln(x^2}) is 6x^5