Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

Secondary 4

Given that \(\frac{\sin y}{{{y}^{2}}+1}=3x\), find an expression of \(\frac{\mathrm{d}y}{\mathrm{d}x}\).

Solution:

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Answer:\(\frac{\mathrm dy}{\mathrm dx}=\frac{3(y^2+1)^2}{(y^2+1)\cos y-2y\sin y}\), where the denominator is nonzero.

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