1. ## Differentiation

Find dy/dx in terms of x if x = t^sqrt(t) , y = e^t

also, dy/dx in terms of theta if x = sin^3 4(theta) , y = cos^3 4(theta)

Thanks!

2. Originally Posted by ose90
Find dy/dx in terms of x if x = t^sqrt(t) , y = e^t
Find:

$\displaystyle \frac{\mathrm{d}x}{\mathrm{d}t}$ Using chain rule and product rule.

And $\displaystyle \frac{\mathrm{d}y}{\mathrm{d}t}$ Using standard differentiation e.g. $\displaystyle \frac{\mathrm{d}(e^x)}{\mathrm{d}x} = e^x$.

Then:

$\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}t} \times \frac{\mathrm{d}t}{\mathrm{d}x}$

Originally Posted by ose90
also, dy/dx in terms of theta if x = sin^3 4(theta) , y = cos^3 4(theta)

Thanks!
Find:

$\displaystyle \frac{\mathrm{d}x}{\mathrm{d}\theta}$ Using chain rule.

And $\displaystyle \frac{\mathrm{d}y}{\mathrm{d}\theta}$ Using chain rule.

Then:

$\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}\theta} \times \frac{\mathrm{d}\theta}{\mathrm{d}x}$