Derivative of $$$6 x e^{3}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(6 x e^{3}\right)$$$.
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 $$$c = 6 e^{3}$$$ and $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(6 x e^{3}\right)\right)} = {\color{red}\left(6 e^{3} \frac{d}{dx} \left(x\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$6 e^{3} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = 6 e^{3} {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dx} \left(6 x e^{3}\right) = 6 e^{3}$$$.
Answer
$$$\frac{d}{dx} \left(6 x e^{3}\right) = 6 e^{3}$$$A