What is the derivative of ((a^x-1))/x ?

The derivative of ((a^x-1))/x is (a^xxln(a)-a^x+1)/(x^2)

What is the first derivative of ((a^x-1))/x ?

The first derivative of ((a^x-1))/x is (a^xxln(a)-a^x+1)/(x^2)

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derivative of

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

\frac{a ^{x} x ln ( a ) - a ^{x} + 1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{a ^{x} - 1}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( a ^{x} - 1 ) x - \frac{d x}{d x} ( a ^{x} - 1 )}{x ^{2}}

\frac{d}{d x} (a^{x} - 1) = a^{x} ln (a)

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

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

Simplify

\frac{a ^{x} ln ( a ) x - 1 \cdot ( a ^{x} - 1 )}{x ^{2}} : \frac{a ^{x} x ln ( a ) - a ^{x} + 1}{x ^{2}}

= \frac{a ^{x} x ln ( a ) - a ^{x} + 1}{x ^{2}}

x^{2} - x + 3

\frac{1}{ln ( x )} - \frac{1}{x} - 1

3 t^{2} + 1

y = \frac{( 5 x + 9 )}{( x - 1 )}

y = x^{3} + x^{2} + x + 1

What is the derivative of ((a^x-1))/x ?
The derivative of ((a^x-1))/x is (a^xxln(a)-a^x+1)/(x^2)
What is the first derivative of ((a^x-1))/x ?
The first derivative of ((a^x-1))/x is (a^xxln(a)-a^x+1)/(x^2)