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Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule a^3^1/2bc^5+(ab^7)^1/2c^3a^9^1/2b^5c. Simplifying. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. 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.