# What is the derivative of f(t) = (t^2-sint , t-1 ) ?

Apr 3, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 t - \cos \left(t\right)$

#### Explanation:

The chain rule is:

$\frac{\mathrm{dy}}{\mathrm{dt}} = \frac{\mathrm{dy}}{\mathrm{dx}} \frac{\mathrm{dx}}{\mathrm{dt}}$

Solving for $\frac{\mathrm{dy}}{\mathrm{dx}}$:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$

Compute the required derivatives:

$\frac{\mathrm{dy}}{\mathrm{dt}} = 2 t - \cos \left(t\right)$

$\frac{\mathrm{dx}}{\mathrm{dt}} = 1$

Divide the derivatives as specified:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 t - \cos \left(t\right)}{1}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 t - \cos \left(t\right)$