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Learn how to solve differential calculus problems step by step online. Find the derivative of ((x^(2n-3)y^(n-2))^3)/(x^(n-8)y^(3n-7)). The power of a product is equal to the product of it's factors raised to the same power. 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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'.
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The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.