Find the derivative of q(x). q(x) = ln(x/e) q′(x) = ______

Simplifying q(x): Let's first simplify the function q(x) = ln(x/e). We can use the property of logarithms that ln(a/b) = ln(a) - ln(b) to rewrite q(x). q(x) = ln(x) - ln(e) Since ln(e) is a constant (ln(e) = 1), we can simplify further: q(x) = ln(x) - 1Finding the derivative of q(x): Now, we need to find the derivative of q(x) with respect to x. The derivative of ln(x) with respect to x is 1/x, and the derivative of a constant is 0. So, q′(x) = d/dx [ln(x) - 1] q′(x) = d/dx [ln(x)] - d/dx [1] q′(x) = 1/x - 0Final derivative of q(x): We can now write the final derivative of q(x): q′(x) = 1/x This is the derivative of the function q(x) = ln(x/e).

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Calculus

Find derivatives using the quotient rule I

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Q. Find the derivative of

q(x)

\newline

q(x) = \ln\left(\frac{x}{e}\right)

\newline

q'\left(x\right) =

______

Simplifying q(x): Let's first simplify the function $q(x) = \ln(\frac{x}{e})$ . We can use the property of logarithms that $\ln(\frac{a}{b}) = \ln(a) - \ln(b)$ to rewrite q(x). $\newline$ $q(x) = \ln(x) - \ln(e)$ $\newline$ Since $\ln(e)$ is a constant ( $\ln(e) = 1$ ), we can simplify further: $\newline$ $q(x) = \ln(x) - 1$
Finding the derivative of q(x): Now, we need to find the derivative of q(x) with respect to x. The derivative of $\ln(x)$ with respect to x is $\frac{1}{x}$ , and the derivative of a constant is $0$ . $\newline$ So, $q'(x) = \frac{d}{dx} [\ln(x) - 1]$ $\newline$ $q'(x) = \frac{d}{dx} [\ln(x)] - \frac{d}{dx} [1]$ $\newline$ $q'(x) = \frac{1}{x} - 0$
Final derivative of q(x): We can now write the final derivative of q(x): $\newline$ q'(x) = \frac{ $1$ }{x} $\newline$ This is the derivative of the function q(x) = \ln\left(\frac{x}{e}\right).