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Popular >

derivative of a^{3x^2}

Solution

\frac{d}{d x} (a^{3 x^{2}})

Solution

6 a^{3 x^{2}} x ln (a)

Solution steps

\frac{d}{d x} (a^{3 x^{2}})

Apply exponent rule:

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

a^{3 x^{2}} = e^{3 x^{2} l n (a)}

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} ln (a)) = 6 x ln (a)

= e^{3 x^{2} l n (a)} \cdot 6 x ln (a)

e^{3 x^{2} l n (a)} = a^{3 x^{2}}

= 6 a^{3 x^{2}} x ln (a)

Popular Examples

taylor-4x^3+3x^2-6x+10 taylor

- 4 x^{3} + 3 x^{2} - 6 x + 10

derivative of y=x^3-14x^2+32x+4 derivative of

y = x^{3} - 14 x^{2} + 32 x + 4

limit as s approaches 0 of (-2s)/(s-3)

s \to 0 lim (\frac{- 2 s}{s - 3})

area y=-x^2+4,y=1-x area

y = - x^{2} + 4, y = 1 - x

integral from 1 to 6 of (sqrt(x^2-1))/x

\int_{1}^{6} \frac{x ^{2} - 1}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of a^{3x^2} ?
The derivative of a^{3x^2} is 6a^{3x^2}xln(a)
What is the first derivative of a^{3x^2} ?
The first derivative of a^{3x^2} is 6a^{3x^2}xln(a)