Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative using the definition
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
- Load more...
Find the derivative of $\ln\left(\frac{1}{x}\right)$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $\ln\left(\frac{1}{x}\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve problems step by step online.
$\lim_{h\to0}\left(\frac{\ln\left(\frac{1}{x+h}\right)-\ln\left(\frac{1}{x}\right)}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of ln(1/x) using the definition. Find the derivative of \ln\left(\frac{1}{x}\right) using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \ln\left(\frac{1}{x}\right). Substituting f(x+h) and f(x) on the limit, we get. Simplify the logarithm \ln\left(\frac{1}{x+h}\right). Factor the polynomial -\ln\left(x+h\right)-\ln\left(\frac{1}{x}\right) by it's greatest common factor (GCF): -1. Simplify the logarithm \ln\left(\frac{1}{x}\right).