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Learn how to solve product rule of differentiation problems step by step online.
$\frac{d}{dx}\left(\cos\left(\frac{2\left(1-\sqrt{x}\right)}{1+\sqrt{x}}\right)\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(cos(2(1-x^1/2)/(1+x^1/2))). Simplifying. 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}}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=.