Categories > differentiation > Differentiation by substitution > 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)

differentiation

Question: 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)


1) $\frac{{{\sin }^{3}}(\alpha +\beta )}{\cos \alpha }$
2) $\cos (\alpha +3\beta )$
3) 0
4) None of these
Solution: Explanation: No Explanation
Differentiation by substitution Higher order derivatives

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