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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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$-\frac{d}{dx}\left(x^2\right)\sin\left(x^2\right)$
Learn how to solve differential equations problems step by step online. Find the derivative of cos(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). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Subtract the values 2 and -1.