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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve definition of derivative problems step by step online.
$derivdef\left(\frac{1}{2}\ln\left(\frac{x}{y}\right)\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of ln((x/y)^1/2) using the definition. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Find the derivative of \frac{1}{2}\ln\left(\frac{x}{y}\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 \frac{1}{2}\ln\left(\frac{x}{y}\right). Substituting f(x+h) and f(x) on the limit, we get. Factor the polynomial \frac{1}{2}\ln\left(\frac{x+h}{y}\right)-\frac{1}{2}\ln\left(\frac{x}{y}\right) by it's greatest common factor (GCF): \frac{1}{2}. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}.