differentiation

Related Questions

• If $y={{\sin }^{2}}\alpha +{{\cos }^{2}}(\alpha +\beta )+2\sin \alpha \sin \beta \cos (\alpha +\beta )$, then $\frac{{{d}^{3}}y}{d{{\alpha }^{3}}}$ is, (keeping $\beta $as constant)

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• If $x = 2\cos t - \cos 2t$,$y = 2\sin t - \sin 2t$, then at $t = \frac{\pi }{4},\frac{{dy}}{{dx}} = $

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• If $y = \sqrt {\frac{{1 + x}}{{1 - x}}} ,$then $\frac{{dy}}{{dx}} = $

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• If $x = y\sqrt {1 - {y^2},} $then $\frac{{dy}}{{dx}} = $

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• If $y=a{{x}^{n+1}}+b{{x}^{-n}}$, then ${{x}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}=$

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