Find the derivative of $\frac{-\frac{413}{100}+\frac{1089}{50}x-\frac{2583}{500}x^2+\frac{91}{297}x^3}{-\frac{413}{100}+\frac{1089}{100}x-\frac{861}{500}x^2+\frac{18}{235}x^3}$
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Learn how to solve differential calculus problems step by step online. Find the derivative of (-413/100+1089/50x-2583/500x^291/297x^3)/(-413/100+1089/100x-861/500x^218/235x^3). Simplifying. 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}}. Simplify the product -(-4.13+21.78x-5.166x^2+\frac{91}{297}x^3). Simplify the product -(21.78x-5.166x^2+\frac{91}{297}x^3).
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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.