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Derivative of $$$2 \sin{\left(t \right)}$$$

The calculator will find the derivative of $$$2 \sin{\left(t \right)}$$$, with steps shown.

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Your Input

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

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 $$$f{\left(t \right)} = \sin{\left(t \right)}$$$:

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

The derivative of the sine is $$$\frac{d}{dt} \left(\sin{\left(t \right)}\right) = \cos{\left(t \right)}$$$:

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

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

Answer

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