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Derivative of $$$2 \sinh{\left(v \right)}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right)$$$.
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 $$$c = 2$$$ and $$$f{\left(v \right)} = \sinh{\left(v \right)}$$$:
$${\color{red}\left(\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)}$$The derivative of the hyperbolic sine is $$$\frac{d}{dv} \left(\sinh{\left(v \right)}\right) = \cosh{\left(v \right)}$$$:
$$2 {\color{red}\left(\frac{d}{dv} \left(\sinh{\left(v \right)}\right)\right)} = 2 {\color{red}\left(\cosh{\left(v \right)}\right)}$$Thus, $$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right) = 2 \cosh{\left(v \right)}$$$.
Answer
$$$\frac{d}{dv} \left(2 \sinh{\left(v \right)}\right) = 2 \cosh{\left(v \right)}$$$A