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