What is the derivative of a^{6x^2} ?

The derivative of a^{6x^2} is 12a^{6x^2}xln(a)

What is the first derivative of a^{6x^2} ?

The first derivative of a^{6x^2} is 12a^{6x^2}xln(a)

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\frac{d}{d x} (a^{6 x^{2}})

12 a^{6 x^{2}} x ln (a)

Solution steps

\frac{d}{d x} (a^{6 x^{2}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

a^{6 x^{2}} = e^{6 x^{2} l n (a)}

= \frac{d}{d x} (e^{6 x^{2} l n (a)})

Apply the chain rule:

e^{6 x^{2} l n (a)} \frac{d}{d x} (6 x^{2} ln (a))

= e^{6 x^{2} l n (a)} \frac{d}{d x} (6 x^{2} ln (a))

\frac{d}{d x} (6 x^{2} ln (a)) = 12 x ln (a)

= e^{6 x^{2} l n (a)} \cdot 12 x ln (a)

e^{6 x^{2} l n (a)} = a^{6 x^{2}}

= 12 a^{6 x^{2}} x ln (a)

What is the derivative of a^{6x^2} ?
The derivative of a^{6x^2} is 12a^{6x^2}xln(a)
What is the first derivative of a^{6x^2} ?
The first derivative of a^{6x^2} is 12a^{6x^2}xln(a)