Derivative of 2*sin(t)

The calculator will find the derivative of

2 \sin{\left(t \right)}

, with steps shown.

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

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

Your Input

Solution

Answer

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