What is the derivative of (9^x-15^{-x}/x) ?

The derivative of (9^x-15^{-x}/x) is (2ln(3)*9^xx+ln(15)*15^{-x}x-9^x+15^{-x})/(x^2)

What is the first derivative of (9^x-15^{-x}/x) ?

The first derivative of (9^x-15^{-x}/x) is (2ln(3)*9^xx+ln(15)*15^{-x}x-9^x+15^{-x})/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{9 ^{x} - 1 5 ^{- x}}{x})

\frac{2 ln ( 3 ) \cdot 9 ^{x} x + ln ( 15 ) \cdot 1 5 ^{- x} x - 9 ^{x} + 1 5 ^{- x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 ^{x} - 1 5 ^{- x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 9 ^{x} - 1 5 ^{- x} ) x - \frac{d x}{d x} ( 9 ^{x} - 1 5 ^{- x} )}{x ^{2}}

\frac{d}{d x} (9^{x} - 1 5^{- x}) = 2 ln (3) \cdot 9^{x} + ln (15) \cdot 1 5^{- x}

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

= \frac{( 2 ln ( 3 ) \cdot 9 ^{x} + ln ( 15 ) \cdot 1 5 ^{- x} ) x - 1 \cdot ( 9 ^{x} - 1 5 ^{- x} )}{x ^{2}}

Simplify

\frac{( 2 ln ( 3 ) \cdot 9 ^{x} + ln ( 15 ) \cdot 1 5 ^{- x} ) x - 1 \cdot ( 9 ^{x} - 1 5 ^{- x} )}{x ^{2}} : \frac{2 ln ( 3 ) \cdot 9 ^{x} x + ln ( 15 ) \cdot 1 5 ^{- x} x - 9 ^{x} + 1 5 ^{- x}}{x ^{2}}

= \frac{2 ln ( 3 ) \cdot 9 ^{x} x + ln ( 15 ) \cdot 1 5 ^{- x} x - 9 ^{x} + 1 5 ^{- x}}{x ^{2}}

(6.3) (4.2)

\int t^{2} - 1 d t

\int \frac{3}{5} - \frac{7}{x} d x

\int \frac{1}{x ^{1.00001}} d x

x \to 0 lim (\frac{x}{4})

What is the derivative of (9^x-15^{-x}/x) ?
The derivative of (9^x-15^{-x}/x) is (2ln(3)*9^xx+ln(15)*15^{-x}x-9^x+15^{-x})/(x^2)
What is the first derivative of (9^x-15^{-x}/x) ?
The first derivative of (9^x-15^{-x}/x) is (2ln(3)*9^xx+ln(15)*15^{-x}x-9^x+15^{-x})/(x^2)