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

The derivative of (xsin^2(x)/(e^x-1)) is ((sin^2(x)+xsin(2x))(e^x-1)-e^xxsin^2(x))/((e^x-1)^2)

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

The first derivative of (xsin^2(x)/(e^x-1)) is ((sin^2(x)+xsin(2x))(e^x-1)-e^xxsin^2(x))/((e^x-1)^2)

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

\frac{( sin ^{2} ( x ) + x sin ( 2 x ) ) ( e ^{x} - 1 ) - e ^{x} x sin ^{2} ( x )}{( e ^{x} - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{( sin ^{2} ( x ) + x sin ( 2 x ) ) ( e ^{x} - 1 ) - e ^{x} x sin ^{2} ( x )}{( e ^{x} - 1 ) ^{2}}

x \to - 1 lim (\frac{x + 1}{x + 1})

\int 3 sin (x) - 2 cos (x) d x

y = 70 x^{- 4}

\int_{0}^{1} sin^{2} (x) d x

\frac{d}{d x} (x + h)

What is the derivative of (xsin^2(x)/(e^x-1)) ?
The derivative of (xsin^2(x)/(e^x-1)) is ((sin^2(x)+xsin(2x))(e^x-1)-e^xxsin^2(x))/((e^x-1)^2)
What is the first derivative of (xsin^2(x)/(e^x-1)) ?
The first derivative of (xsin^2(x)/(e^x-1)) is ((sin^2(x)+xsin(2x))(e^x-1)-e^xxsin^2(x))/((e^x-1)^2)