What is the derivative of f(x)=(5^x)/x ?

The derivative of f(x)=(5^x)/x is (ln(5)*5^xx-5^x)/(x^2)

What is the first derivative of f(x)=(5^x)/x ?

The first derivative of f(x)=(5^x)/x is (ln(5)*5^xx-5^x)/(x^2)

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derivative of

f (x) = \frac{5 ^{x}}{x}

\frac{ln ( 5 ) \cdot 5 ^{x} x - 5 ^{x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 ^{x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 ^{x} ) x - \frac{d x}{d x} 5 ^{x}}{x ^{2}}

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

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

= \frac{5 ^{x} ln ( 5 ) x - 1 \cdot 5 ^{x}}{x ^{2}}

Simplify

= \frac{ln ( 5 ) \cdot 5 ^{x} x - 5 ^{x}}{x ^{2}}

y = \frac{1}{5 x}

ln (n + 1)

\frac{d}{d o} (7 o + (- 18) 0 - 61 + (- 9) 1)

1 - a

\frac{2}{( x ^{2} - 1 )}

What is the derivative of f(x)=(5^x)/x ?
The derivative of f(x)=(5^x)/x is (ln(5)*5^xx-5^x)/(x^2)
What is the first derivative of f(x)=(5^x)/x ?
The first derivative of f(x)=(5^x)/x is (ln(5)*5^xx-5^x)/(x^2)