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Popular >

derivative of 3^{ln(x})

Solution

\frac{d}{d x} (3^{l n (x)})

Solution

ln (3) x^{l n (3) - 1}

Solution steps

\frac{d}{d x} (3^{l n (x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x) ln (3)) = \frac{ln ( 3 )}{x}

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

Simplify

e^{l n (x) l n (3)} \frac{ln ( 3 )}{x} : ln (3) x^{l n (3) - 1}

= ln (3) x^{l n (3) - 1}

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Frequently Asked Questions (FAQ)

What is the derivative of 3^{ln(x}) ?
The derivative of 3^{ln(x}) is ln(3)x^{ln(3)-1}
What is the first derivative of 3^{ln(x}) ?
The first derivative of 3^{ln(x}) is ln(3)x^{ln(3)-1}