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If y = xsin x + 2020, then find dy/dx. |
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Answer» y = xsinx + 2020 \(\therefore\) \(\frac{dy}{dx}=\frac{d}{dx}x^{sin x}\)---(1) \((\because\frac{d}{dx}constant=0)\) Let xsinx = z Then sin log x = log z (by taking log on both sides) ⇒ \(\frac{sin x}x+log x cos x=\frac1z\frac{dz}{dx}\) (on differentiating both sides w.r.t. x) \(\therefore\) \(\frac{dz}{dx}=z(\frac{sin x}x+log x\,cosx)\) ⇒ \(\frac{d}{dx}x\,sin x\) = xsinx(\(\frac{sinx}x\) + cos x log x) (From (1)) |
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