calculus · worked example

Solve x · cos(x)

Method: product rule. Verified step-by-step solution with our free AI math solver.
Problem

ddx(xcos⁡x)\frac{d}{dx}(x \cos x)

Step-by-step solution

  1. Apply (fg)′=f′g+fg′(fg)' = f'g + fg' with f=xf = x, g=cos⁡xg = \cos x.

  2. f′=1f' = 1, g′=−sin⁡xg' = -\sin x.

  3. Result: cos⁡x−xsin⁡x\cos x - x\sin x.

Answer

cos⁡(x)−xsin⁡(x)\cos(x) - x\sin(x)

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