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Popular >

derivative of e^{log_{3}(x})

Solution

\frac{d}{d x} (e^{l o g_{3} (x)})

Solution

\frac{e ^{l o g_{3} (x)}}{ln ( 3 ) x}

Solution steps

\frac{d}{d x} (e^{l o g_{3} (x)})

Apply the chain rule:

e^{l o g_{3} (x)} \frac{d}{d x} (lo g_{3} (x))

= e^{l o g_{3} (x)} \frac{d}{d x} (lo g_{3} (x))

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{x ln ( 3 )}

= e^{l o g_{3} (x)} \frac{1}{x ln ( 3 )}

Simplify

e^{l o g_{3} (x)} \frac{1}{x ln ( 3 )} : \frac{e ^{l o g_{3} (x)}}{ln ( 3 ) x}

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

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\int_{- 6}^{6} (6 - ∣ x ∣) d x

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integral of 20e^{5x}

\int 20 e^{5 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of e^{log_{3}(x}) ?
The derivative of e^{log_{3}(x}) is (e^{log_{3}(x)})/(ln(3)x)
What is the first derivative of e^{log_{3}(x}) ?
The first derivative of e^{log_{3}(x}) is (e^{log_{3}(x)})/(ln(3)x)