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Find the derivative of $y^{\ln\left|'y\right|}$ 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 $y^{\ln\left|'y\right|}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{y^{\ln\left|'y\right|}-y^{\ln\left|'y\right|}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of x=y^ln(abs('y)) using the definition. Find the derivative of y^{\ln\left|'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 y^{\ln\left|'y\right|}. Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms y^{\ln\left|'y\right|} and -y^{\ln\left|'y\right|}. Zero divided by anything is equal to zero. The limit of a constant is just the constant.