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

Oct 14, 2017

$\left(\frac{2 \ln t}{t} - 1 , \cos t - t \sin t\right)$

#### Explanation:

Interpreting the problem statement as the derivative of a vector, where each component is a function of $t$. We can simply find the derivative of each of these functions independently.

The x component is ${f}_{x} \left(t\right) = {\left(\ln t\right)}^{2} - t$, so its derivative is:

${f}_{x} ' \left(t\right) = \frac{2 \ln t}{t} - 1$

The y component is ${f}_{y} \left(t\right) = t \cos t$, and its derivative is:

${f}_{y} ' \left(t\right) = \cos t - t \sin \left(t\right)$

GOOD LUCK