Question

If the tangent to a curve at a point (x, y) is equally inclined to the coordinates axes then write the value of $\frac{dy}{dx}$.

Answer 1

Because the tangent to the curve at (x, y) is equally inclined to the coordinate axes, the angle made by the tangent with the axes can be $\pm 45°$.
$\text{∴}\frac{dy}{dx}\text{=Slope of the tangent=tan}\left(\pm 45\right)\text{=±1}$