What is the derivative of (t^2+1)/(t^2-1) ?

The derivative of (t^2+1)/(t^2-1) is -(4t)/((t^2-1)^2)

What is the first derivative of (t^2+1)/(t^2-1) ?

The first derivative of (t^2+1)/(t^2-1) is -(4t)/((t^2-1)^2)

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derivative of

\frac{t ^{2} + 1}{t ^{2} - 1}

- \frac{4 t}{( t ^{2} - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 t ( t ^{2} - 1 ) - 2 t ( t ^{2} + 1 )}{( t ^{2} - 1 ) ^{2}} : - \frac{4 t}{( t ^{2} - 1 ) ^{2}}

= - \frac{4 t}{( t ^{2} - 1 ) ^{2}}

w \to 0 lim (\frac{e ^{2 w} - ( 1 + w )}{w ^{2}})

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

\int \frac{2 x + 3}{x ^{2} + 3 x - 5} d x

\int ln (\frac{1}{x}) d x

What is the derivative of (t^2+1)/(t^2-1) ?
The derivative of (t^2+1)/(t^2-1) is -(4t)/((t^2-1)^2)
What is the first derivative of (t^2+1)/(t^2-1) ?
The first derivative of (t^2+1)/(t^2-1) is -(4t)/((t^2-1)^2)