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Derivative of $$$9 x e^{2} - 4$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(9 x e^{2} - 4\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(9 x e^{2} - 4\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(9 x e^{2}\right) - \frac{d}{dx} \left(4\right)\right)}$$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 $$$c = 9 e^{2}$$$ and $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(9 x e^{2}\right)\right)} - \frac{d}{dx} \left(4\right) = {\color{red}\left(9 e^{2} \frac{d}{dx} \left(x\right)\right)} - \frac{d}{dx} \left(4\right)$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$9 e^{2} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} - \frac{d}{dx} \left(4\right) = 9 e^{2} {\color{red}\left(1\right)} - \frac{d}{dx} \left(4\right)$$The derivative of a constant is $$$0$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(4\right)\right)} + 9 e^{2} = - {\color{red}\left(0\right)} + 9 e^{2}$$Thus, $$$\frac{d}{dx} \left(9 x e^{2} - 4\right) = 9 e^{2}$$$.
Answer
$$$\frac{d}{dx} \left(9 x e^{2} - 4\right) = 9 e^{2}$$$A