Learn how to solve numerical value of an algebraic expression problems step by step online. Find the derivative of ((x^2)/(6x^2-3))^(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}. Since the exponent is negative, we can invert the fraction. 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}}. Multiplying fractions \frac{1}{3} \times \frac{\frac{d}{dx}\left(x^2\right)\left(6x^2-3\right)-x^2\frac{d}{dx}\left(6x^2-3\right)}{\left(6x^2-3\right)^2}.

Find the derivative of ((x^2)/(6x^2-3))^(1/3)