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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$\frac{1}{3}\ln\left(\frac{3x}{x+2}\right)^{-\frac{2}{3}}\frac{d}{dx}\left(\ln\left(\frac{3x}{x+2}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln((3x)/(x+2))^1/3). 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 logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). The derivative of a sum of two or more functions is the sum of the derivatives of each function.