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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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$-\frac{d}{dx}\left(\pi x^2\right)\sin\left(\pi x^2\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(cos(pix^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 product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the constant function (\pi ) is equal to zero. Any expression multiplied by 0 is equal to 0.