What is the derivative of (10^x/(10^x+4)) ?

The derivative of (10^x/(10^x+4)) is (ln(10)*5^x*2^{x+2})/((10^x+4)^2)

What is the first derivative of (10^x/(10^x+4)) ?

The first derivative of (10^x/(10^x+4)) is (ln(10)*5^x*2^{x+2})/((10^x+4)^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{1 0 ^{x}}{1 0 ^{x} + 4})

\frac{ln ( 10 ) \cdot 5 ^{x} \cdot 2 ^{x + 2}}{( 1 0 ^{x} + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 0 ^{x}}{1 0 ^{x} + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 0 ^{x} ) ( 1 0 ^{x} + 4 ) - \frac{d}{d x} ( 1 0 ^{x} + 4 ) 1 0 ^{x}}{( 1 0 ^{x} + 4 ) ^{2}}

\frac{d}{d x} (1 0^{x}) = 1 0^{x} ln (10)

\frac{d}{d x} (1 0^{x} + 4) = ln (10) \cdot 1 0^{x}

= \frac{1 0 ^{x} ln ( 10 ) ( 1 0 ^{x} + 4 ) - ln ( 10 ) \cdot 1 0 ^{x} \cdot 1 0 ^{x}}{( 1 0 ^{x} + 4 ) ^{2}}

Simplify

\frac{1 0 ^{x} ln ( 10 ) ( 1 0 ^{x} + 4 ) - ln ( 10 ) \cdot 1 0 ^{x} \cdot 1 0 ^{x}}{( 1 0 ^{x} + 4 ) ^{2}} : \frac{ln ( 10 ) \cdot 5 ^{x} \cdot 2 ^{x + 2}}{( 1 0 ^{x} + 4 ) ^{2}}

= \frac{ln ( 10 ) \cdot 5 ^{x} \cdot 2 ^{x + 2}}{( 1 0 ^{x} + 4 ) ^{2}}

\int_{0}^{2 π} x sin (x) cos (x) d x

\frac{1}{s ^{2} + 6 s + 7}

\frac{d y}{d x} = \frac{x}{x ^{2} - 7 x + 12}, y (5) = 0

\frac{d}{d x} (e^{- 6 x^{2}})

x \to \infty lim (6 + \frac{1}{x})

What is the derivative of (10^x/(10^x+4)) ?
The derivative of (10^x/(10^x+4)) is (ln(10)*5^x*2^{x+2})/((10^x+4)^2)
What is the first derivative of (10^x/(10^x+4)) ?
The first derivative of (10^x/(10^x+4)) is (ln(10)*5^x*2^{x+2})/((10^x+4)^2)