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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{5x^2}\frac{d}{dx}\left(5x^2\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(ln(5x^2)). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the constant function (5) is equal to zero. Any expression multiplied by 0 is equal to 0.