Find the derivative using the quotient rule $\frac{d}{dx}\left(\frac{\sin\left(x\right)\left(3\sin\left(x\right)^2+2\cos\left(x\right)^2-4+2\cos\left(x\right)\right)}{8\left(1-\cos\left(x\right)\right)^{\frac{5}{2}}}\right)$
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Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule d/dx((sin(x)(3sin(x)^2+2cos(x)^2+-42cos(x)))/(8(1-cos(x))^(5/2))). Simplifying. 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}}. The power of a product is equal to the product of it's factors raised to the same power.
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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.