What is the derivative of (2^x/(3x-1)) ?

The derivative of (2^x/(3x-1)) is (2^xln(2)(3x-1)-3*2^x)/((3x-1)^2)

What is the first derivative of (2^x/(3x-1)) ?

The first derivative of (2^x/(3x-1)) is (2^xln(2)(3x-1)-3*2^x)/((3x-1)^2)

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\frac{d}{d x} (\frac{2 ^{x}}{3 x - 1})

\frac{2 ^{x} ln ( 2 ) ( 3 x - 1 ) - 3 \cdot 2 ^{x}}{( 3 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 ^{x}}{3 x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 ^{x} ) ( 3 x - 1 ) - \frac{d}{d x} ( 3 x - 1 ) 2 ^{x}}{( 3 x - 1 ) ^{2}}

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

\frac{d}{d x} (3 x - 1) = 3

= \frac{2 ^{x} ln ( 2 ) ( 3 x - 1 ) - 3 \cdot 2 ^{x}}{( 3 x - 1 ) ^{2}}

\int \frac{4 x + 7}{( 3 x + 2 ) ( x - 5 )} d x

\int x^{2} ln (8 x) d x

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

\int sin^{3} (θ) d θ

What is the derivative of (2^x/(3x-1)) ?
The derivative of (2^x/(3x-1)) is (2^xln(2)(3x-1)-3*2^x)/((3x-1)^2)
What is the first derivative of (2^x/(3x-1)) ?
The first derivative of (2^x/(3x-1)) is (2^xln(2)(3x-1)-3*2^x)/((3x-1)^2)