Find dx dy in the following: 2x + 3y = - Vidyadip

Question

Find $\frac{\text{dx}}{{\text{dy}}}$ in the following:
$2\text{x} + 3\text{y} = \sin\text{x}$

✓

Answer

The given relationship is $2\text{x} + 3\text{y} = \sin\text{x}$
Differentiating this relationship with respect to x, we obtain
$\frac{\text{d}}{\text{dx}}(2\text{x} + 3\text{y}) = \frac{\text{d}}{\text{dx}}(\sin\text{x)}$
$\therefore\ \frac{\text{d}}{\text{dx}}(2\text{x}) + \frac{\text{d}}{\text{dx}}(3\text{y)} = \cos\text{x}$
$\Rightarrow 2 + 3\frac{\text{dy}}{\text{dx}}= \cos\text{x}$
$\Rightarrow 3 \frac{\text{dy}}{\text{dx}}= \cos\text{x} - 2$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{ \cos\text{x} - 2}{3}$

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