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Popular >

derivative of 6^{x^2}

Solution

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

Solution

ln (6) \cdot 3^{x^{2}} \cdot 2^{x^{2} + 1} x

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{x^{2} l n (6)} \cdot 2 ln (6) x : ln (6) \cdot 3^{x^{2}} \cdot 2^{x^{2} + 1} x

= ln (6) \cdot 3^{x^{2}} \cdot 2^{x^{2} + 1} x

Popular Examples

derivative of ((6x^2+8x+2)/(sqrt(x)))

\frac{d}{d x} (\frac{( 6 x ^{2} + 8 x + 2 )}{x})

(\partial)/(\partial x)(30y^4sin(2x))

\frac{\partial}{\partial x} (30 y^{4} sin (2 x))

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derivative of xsin(4x)

\frac{d}{d x} (x sin (4 x))

tangent of f(x)=cos((pix)/2),\at x=0.4 tangent of

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Frequently Asked Questions (FAQ)

What is the derivative of 6^{x^2} ?
The derivative of 6^{x^2} is ln(6)*3^{x^2}*2^{x^2+1}x
What is the first derivative of 6^{x^2} ?
The first derivative of 6^{x^2} is ln(6)*3^{x^2}*2^{x^2+1}x