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

The derivative of (t^2+1)/(t^2) is -2/(t^3)

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

The first derivative of (t^2+1)/(t^2) is -2/(t^3)

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derivative of

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

- \frac{2}{t ^{3}}

Solution steps

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

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

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

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

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

Simplify

\frac{2 t t ^{2} - 2 t ( t ^{2} + 1 )}{( t ^{2} ) ^{2}} : - \frac{2}{t ^{3}}

= - \frac{2}{t ^{3}}

\frac{d}{d a} (3 cos^{2} (a) - sin^{2} (a))

x tan (x) + 1

y = \frac{x + 2}{x ^{2}}

- 9 sin^{5} (x)

\frac{x ^{n + 1}}{( n + 1 )}

What is the derivative of (t^2+1)/(t^2) ?
The derivative of (t^2+1)/(t^2) is -2/(t^3)
What is the first derivative of (t^2+1)/(t^2) ?
The first derivative of (t^2+1)/(t^2) is -2/(t^3)