Given y = 2e^x + 3 x − 5 + 1/x2

Question

ScanSolve AI Tutor · Accepted Answer

Here's the derivative for the given function:

Given $y = 2e^x + 3 \ln x - 5 + \frac{1}{x^2}$

Rewrite the expression, converting the fraction to a term with a negative exponent.
$y = 2e^x + 3 \ln x - 5 + x^{-2}$
Differentiate each term using the following rules
- $\frac{d}{dx}(e^x) = e^x$
- $\frac{d}{dx}(\ln x) = \frac{1}{x}$
- $\frac{d}{dx}(c) = 0$ (for a constant $c$ )
- $\frac{d}{dx}(x^n) = nx^{n-1}$
$\frac{dy}{dx} = \frac{d}{dx}(2e^x) + \frac{d}{dx}(3 \ln x) - \frac{d}{dx}(5) + \frac{d}{dx}(x^{-2})$ $\frac{dy}{dx} = 2e^x + 3\left(\frac{1}{x}\right) - 0 + (-2)x^{-2-1}$ $\frac{dy}{dx} = 2e^x + \frac{3}{x} - 2x^{-3}$
Rewrite the term with the negative exponent as a fraction.
$\frac{dy}{dx} = 2e^x + \frac{3}{x} - \frac{2}{x^3}$
The final answer is $2e^x + \frac{3}{x} - \frac{2}{x^3}$ .

Given y = 2e^x + 3 x - 5 + (1)/(x2)