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Derivative of $$$2 - \frac{1}{t^{2}}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dt} \left(2 - \frac{1}{t^{2}}\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dt} \left(2 - \frac{1}{t^{2}}\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(2\right) - \frac{d}{dt} \left(\frac{1}{t^{2}}\right)\right)}$$Apply the power rule $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ with $$$n = -2$$$:
$$- {\color{red}\left(\frac{d}{dt} \left(\frac{1}{t^{2}}\right)\right)} + \frac{d}{dt} \left(2\right) = - {\color{red}\left(- \frac{2}{t^{3}}\right)} + \frac{d}{dt} \left(2\right)$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{d}{dt} \left(2\right)\right)} + \frac{2}{t^{3}} = {\color{red}\left(0\right)} + \frac{2}{t^{3}}$$Thus, $$$\frac{d}{dt} \left(2 - \frac{1}{t^{2}}\right) = \frac{2}{t^{3}}$$$.
Answer
$$$\frac{d}{dt} \left(2 - \frac{1}{t^{2}}\right) = \frac{2}{t^{3}}$$$A
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