
Differentiation
I believe and i am hoping i've completed the following question is correctly... Please confirm this for me.. Many thanks in advance..
Differentate the following
y= 3 sin (2x^2)
t= (2x^2) therefore y=3 sin t
dt/dx = 4x dy/dt= 3 cos t
dy/dx= dy/dt * dt/dx
= 3 cos t * 4x
= 3 cos (2x^2) (4x)
Is this correct...
Again mant thanks...

Correct except for one thing:
$\displaystyle \frac{dy}{dt} = 3 \cos t$

This problem can also be solved by using the chain rule, which will give you the same answer as you listed above, and you can avoid the necessity of substituting.