Derivative of $$$1 - t^{4}$$$
The calculator will find the derivative of $$$1 - t^{4}$$$, with steps shown.
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Your Input
Find $$$\frac{d}{dt} \left(1 - t^{4}\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dt} \left(1 - t^{4}\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(1\right) - \frac{d}{dt} \left(t^{4}\right)\right)}$$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, $$$\frac{d}{dt} \left(1 - t^{4}\right) = - 4 t^{3}$$$.
Answer
$$$\frac{d}{dt} \left(1 - t^{4}\right) = - 4 t^{3}$$$A