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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(\sqrt[5]{4x-5}\right)\ln\left(\frac{2x}{\sqrt[3]{4x-5}}\right)+\sqrt[5]{4x-5}\frac{d}{dx}\left(\ln\left(\frac{2x}{\sqrt[3]{4x-5}}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of d/dx((4x-5)^1/5ln((2x)/((4x-5)^1/3))). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. 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}. Divide fractions \frac{1}{\frac{2x}{\sqrt[3]{4x-5}}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.