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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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$-\frac{d}{dx}\left(x^3+5x\right)\sin\left(x^3+5x\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of cos(x^3+5x). 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 derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.