What is the derivative of (x^2)/(ln(3^x)) ?

The derivative of (x^2)/(ln(3^x)) is 1/(ln(3))

What is the first derivative of (x^2)/(ln(3^x)) ?

The first derivative of (x^2)/(ln(3^x)) is 1/(ln(3))

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derivative of

\frac{x ^{2}}{ln ( 3 ^{x} )}

\frac{1}{ln ( 3 )}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{ln ( 3 ^{x} )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) ln ( 3 ^{x} ) - \frac{d}{d x} ( ln ( 3 ^{x} ) ) x ^{2}}{( ln ( 3 ^{x} ) ) ^{2}}

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

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

= \frac{2 x ln ( 3 ^{x} ) - ln ( 3 ) x ^{2}}{( ln ( 3 ^{x} ) ) ^{2}}

Simplify

\frac{2 x ln ( 3 ^{x} ) - ln ( 3 ) x ^{2}}{ln ^{2} ( 3 ^{x} )} : \frac{1}{ln ( 3 )}

= \frac{1}{ln ( 3 )}

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What is the derivative of (x^2)/(ln(3^x)) ?
The derivative of (x^2)/(ln(3^x)) is 1/(ln(3))
What is the first derivative of (x^2)/(ln(3^x)) ?
The first derivative of (x^2)/(ln(3^x)) is 1/(ln(3))