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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Graph

Popular Examples

integral of 1/(xsqrt(16x^2-1))

\int \frac{1}{x 16 x ^{2} - 1} d x

derivative of f(x)= t/((t-7)^2)derivative of

f (x) = \frac{t}{( t - 7 ) ^{2}}

derivative of ln(e^{2x}+1)

\frac{d}{d x} (ln (e^{2 x} + 1))

limit as x approaches infinity of (1+1/x)^{x+3}

x \to \infty lim ((1 + \frac{1}{x})^{x + 3})

y^{^{''}} = - k y

Frequently Asked Questions (FAQ)

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