Derivative of sqrt(3)*sinh(v)/2

The calculator will find the derivative of

\frac{\sqrt{3} \sinh{\left(v \right)}}{2}

, with steps shown.

Your Input

Find $\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right)$ .

Solution

Apply the constant multiple rule $\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$ with $c = \frac{\sqrt{3}}{2}$ and $f{\left(v \right)} = \sinh{\left(v \right)}$ :

{\color{red}\left(\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right)\right)} = {\color{red}\left(\frac{\sqrt{3}}{2} \frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)}

The derivative of the hyperbolic sine is $\frac{d}{dv} \left(\sinh{\left(v \right)}\right) = \cosh{\left(v \right)}$ :

\frac{\sqrt{3} {\color{red}\left(\frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)}}{2} = \frac{\sqrt{3} {\color{red}\left(\cosh{\left(v \right)}\right)}}{2}

Thus, $\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right) = \frac{\sqrt{3} \cosh{\left(v \right)}}{2}$ .

Answer

$\frac{d}{dv} \left(\frac{\sqrt{3} \sinh{\left(v \right)}}{2}\right) = \frac{\sqrt{3} \cosh{\left(v \right)}}{2}$ A

Derivative of 3sinh⁡(v)2\frac{\sqrt{3} \sinh{\left(v \right)}}{2}23​sinh(v)​

Your Input

Solution

Answer

Derivative of $\frac{\sqrt{3} \sinh{\left(v \right)}}{2}$