Derivative of $$$3 \cos{\left(x \right)}$$$
The calculator will find the derivative of $$$3 \cos{\left(x \right)}$$$, with steps shown.
Related calculator: Derivative Calculator
Solution
Apply the constant multiple rule $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ with $$$c = 3$$$ and $$$f{\left(x \right)} = \cos{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(3 \cos{\left(x \right)}\right)\right)} = {\color{red}\left(3 \frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)}$$The derivative of the cosine is $$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$:
$$3 {\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} = 3 {\color{red}\left(- \sin{\left(x \right)}\right)}$$Thus, $$$\frac{d}{dx} \left(3 \cos{\left(x \right)}\right) = - 3 \sin{\left(x \right)}$$$.
Answer
$$$\frac{d}{dx} \left(3 \cos{\left(x \right)}\right) = - 3 \sin{\left(x \right)}$$$A