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Popular >

derivative of (2^x)/(3x-1)

Solution

derivative of

\frac{2 ^{x}}{3 x - 1}

Solution

\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}}

Popular Examples

integral from 0 to 5 of x/(sqrt(1+3x))

\int_{0}^{5} \frac{x}{1 + 3 x} d x

integral of 1/(xsqrt(x^2-1))

\int \frac{1}{x x ^{2} - 1} d x

integral of 1/(x/2-3)cos(x/2-3)

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

derivative of (log_{2}(x))^2 derivative of

(lo g_{2} (x))^{2}

derivative of ((3x^7-7x^2+113)/((5x^3)))

\frac{d}{d x} (\frac{( 3 x ^{7} - 7 x ^{2} + 113 )}{( 5 x ^{3} )})

Frequently Asked Questions (FAQ)

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)