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Learn how to solve differential calculus problems step by step online. Find the derivative of (cos(x)^2-(1-sin(x)))/(cos(x)-cos(x)sin(x)). Simplify the product -(1-\sin\left(x\right)). 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 -(\cos\left(x\right)^2-1+\sin\left(x\right)). Simplify the product -(-1+\sin\left(x\right)).
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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.