CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

4. $\frac{3\text{t}}{2}$

Solution:

$\text{x}=\text{t}^2\Rightarrow\frac{\text{dx}}{\text{dt}}=2\text{t}$

$\text{y}=\text{t}^3\Rightarrow\frac{\text{dy}}{\text{dt}}=3\text{t}^2$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{3\text{t}^2}{2\text{t}}$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{3\text{t}}{2}$