# Derivative of $2 t$

The calculator will find the derivative of $2 t$, with steps shown.

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Find $\frac{d}{dt} \left(2 t\right)$.

### Solution

Apply the constant multiple rule $\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$ with $c = 2$ and $f{\left(t \right)} = t$:

$${\color{red}\left(\frac{d}{dt} \left(2 t\right)\right)} = {\color{red}\left(2 \frac{d}{dt} \left(t\right)\right)}$$

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

$$2 {\color{red}\left(\frac{d}{dt} \left(t\right)\right)} = 2 {\color{red}\left(1\right)}$$

Thus, $\frac{d}{dt} \left(2 t\right) = 2$.

$\frac{d}{dt} \left(2 t\right) = 2$A