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$\frac{d}{dx}\left(\frac{\frac{\frac{a}{\sqrt{3}}}{\sqrt[3]{\left(\sqrt{3}bx-x^2\right)^{5}}}}{\sqrt[3]{\left(\sqrt{3}b+4x\right)^{2}}}\right)=0$
Learn how to solve differential calculus problems step by step online. Find the implicit derivative d/dx(((a/(3^1/2))/((3^1/2bx-x^2)^(5/3)))/((3^1/2b+4x)^2/3))=0. Simplifying. Simplify the derivative by applying the properties of logarithms. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The power of a product is equal to the product of it's factors raised to the same power.