Derivative of $$$t^{4} - 1$$$

The calculator will find the derivative of $$$t^{4} - 1$$$, with steps shown.

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Your Input

Find $$$\frac{d}{dt} \left(t^{4} - 1\right)$$$.

Solution

The derivative of a sum/difference is the sum/difference of derivatives:

$${\color{red}\left(\frac{d}{dt} \left(t^{4} - 1\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(t^{4}\right) - \frac{d}{dt} \left(1\right)\right)}$$

Apply the power rule $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ with $$$n = 4$$$:

$${\color{red}\left(\frac{d}{dt} \left(t^{4}\right)\right)} - \frac{d}{dt} \left(1\right) = {\color{red}\left(4 t^{3}\right)} - \frac{d}{dt} \left(1\right)$$

The derivative of a constant is $$$0$$$:

$$4 t^{3} - {\color{red}\left(\frac{d}{dt} \left(1\right)\right)} = 4 t^{3} - {\color{red}\left(0\right)}$$

Thus, $$$\frac{d}{dt} \left(t^{4} - 1\right) = 4 t^{3}$$$.

Answer

$$$\frac{d}{dt} \left(t^{4} - 1\right) = 4 t^{3}$$$A