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)

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\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}}

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)