Question:
If the tangent to a curve at a point $(x, y)$ is equally inclined to the coordinate axes, then write the value of
$\frac{d y}{d x}$.
Solution:
Given that the tangent to a curve at a point $(x, y)$ is equally inclined to the coordinate axes.
$\Rightarrow$ The angle made by the tangent with the axes can be $\pm 45^{\circ} .$
$\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\tan \pm 45^{\circ}=\pm 1$
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