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Calculating the natural logarithm of $1$
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$derivdef\left(\ln\left(e^{4x}\right)+0\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of ln(e^(4x))-ln(1) using the definition. Calculating the natural logarithm of 1. x+0=x, where x is any expression. Apply the formula: \ln\left(e^x\right)=x, where x=4x. Find the derivative of 4x 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 4x. Substituting f(x+h) and f(x) on the limit, we get.