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Derivative of $$$- \frac{\ln\left(7\right)}{x}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(- \frac{\ln\left(7\right)}{x}\right)$$$.
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 $$$c = - \ln\left(7\right)$$$ and $$$f{\left(x \right)} = \frac{1}{x}$$$:
$${\color{red}\left(\frac{d}{dx} \left(- \frac{\ln\left(7\right)}{x}\right)\right)} = {\color{red}\left(- \ln\left(7\right) \frac{d}{dx} \left(\frac{1}{x}\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = -1$$$:
$$- \ln\left(7\right) {\color{red}\left(\frac{d}{dx} \left(\frac{1}{x}\right)\right)} = - \ln\left(7\right) {\color{red}\left(- \frac{1}{x^{2}}\right)}$$Thus, $$$\frac{d}{dx} \left(- \frac{\ln\left(7\right)}{x}\right) = \frac{\ln\left(7\right)}{x^{2}}$$$.
Answer
$$$\frac{d}{dx} \left(- \frac{\ln\left(7\right)}{x}\right) = \frac{\ln\left(7\right)}{x^{2}}$$$A