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calculus · worked example

Solve x · cos(x) = cos(x) - xsin(x)

Method: ضرب کا قاعدہ. 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. f=xf = x, g=cos⁡xg = \cos x کے ساتھ (fg)′=f′g+fg′(fg)' = f'g + fg' استعمال کریں۔

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

  3. نتیجہ: cos⁡x−xsin⁡x\cos x - x\sin x۔

Answer

cos⁡(x)−xsin⁡(x)\cos(x) - x\sin(x)

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