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$\frac{d}{dx}\left(\left(\sqrt{\ln\left(8x^2+3x\right)^{3}}\right)^3\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ln(8x^2+3x)^(3/2)^3. Simplifying. Simplify the derivative by applying the properties of logarithms. 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}.