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Popular >

derivative of 12^{9x}

Solution

derivative of

1 2^{9 x}

Solution

ln (12) \cdot 26214 4^{x} \cdot 3^{9 x + 2}

Solution steps

\frac{d}{d x} (1 2^{9 x})

Apply exponent rule:

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

1 2^{9 x} = e^{9 x l n (12)}

= \frac{d}{d x} (e^{9 x l n (12)})

Apply the chain rule:

e^{9 x l n (12)} \frac{d}{d x} (9 x ln (12))

= e^{9 x l n (12)} \frac{d}{d x} (9 x ln (12))

\frac{d}{d x} (9 x ln (12)) = 9 ln (12)

= e^{9 x l n (12)} \cdot 9 ln (12)

Simplify

e^{9 x l n (12)} \cdot 9 ln (12) : ln (12) \cdot 26214 4^{x} \cdot 3^{9 x + 2}

= ln (12) \cdot 26214 4^{x} \cdot 3^{9 x + 2}

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Frequently Asked Questions (FAQ)

What is the derivative of 12^{9x} ?
The derivative of 12^{9x} is ln(12)*262144^x*3^{9x+2}
What is the first derivative of 12^{9x} ?
The first derivative of 12^{9x} is ln(12)*262144^x*3^{9x+2}