What is the derivative of f(x)=(3^x)/x ?

The derivative of f(x)=(3^x)/x is (ln(3)*3^xx-3^x)/(x^2)

What is the first derivative of f(x)=(3^x)/x ?

The first derivative of f(x)=(3^x)/x is (ln(3)*3^xx-3^x)/(x^2)

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derivative of

f (x) = \frac{3 ^{x}}{x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

What is the derivative of f(x)=(3^x)/x ?
The derivative of f(x)=(3^x)/x is (ln(3)*3^xx-3^x)/(x^2)
What is the first derivative of f(x)=(3^x)/x ?
The first derivative of f(x)=(3^x)/x is (ln(3)*3^xx-3^x)/(x^2)