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Derivative of $$$2 t$$$

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

Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps

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Your Input

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

Answer

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

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function