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The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if $f(x) = \cos(x)$, then $f'(x) = -\sin(x)\cdot D_x(x)$
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$-\frac{d}{dx}\left(\frac{-\left(1-x^2\right)}{1+x^2}\right)\sin\left(\frac{-\left(1-x^2\right)}{1+x^2}\right)$
Learn how to solve problems step by step online. Find the derivative of cos((-(1-x^2))/(1+x^2)). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). 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}}. Multiply -1 times -1. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.