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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

sum from n=1 to infinity of (5nln(n))/(6^n)

n = 1 \sum \infty \frac{5 n ln ( n )}{6 ^{n}}

derivative of (5+csc(x))/(9-csc(x))derivative of

\frac{5 + csc ( x )}{9 - csc ( x )}

(1+t^2)(dy)/(dt)+2ty=t

(1 + t^{2}) \frac{d y}{d t} + 2 t y = t

integral of \sqrt[3]{7t}

derivative of (x^2)/(sqrt(x^2+5))derivative of

\frac{x ^{2}}{x ^{2} + 5}

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)