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Derivative of 2t2 t

The calculator will find the derivative of 2t2 t, with steps shown.

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Your Input

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

Solution

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

(ddt(2t))=(2ddt(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 ddt(tn)=ntn−1\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1} with n=1n = 1, in other words, ddt(t)=1\frac{d}{dt} \left(t\right) = 1:

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

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

Answer

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

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