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Popular >

derivative of a^{6x^2}

Solution

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

Solution

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)

Graph

Popular Examples

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\int \frac{x ^{2}}{4 x} d x

x^{2} y^{^{'}} + 3 x y = e^{x}

2y^{''}-2y^'+13y=0

2 y^{^{''}} - 2 y^{^{'}} + 13 y = 0

derivative of-4sin^3(3x)

\frac{d}{d x} (- 4 sin^{3} (3 x))

integral of 1/(5000x-x^2)

\int \frac{1}{5000 x - x ^{2}} d x

Frequently Asked Questions (FAQ)

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)