# Math Help - Differentiation

1. ## 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...

2. Correct except for one thing:

$\frac{dy}{dt} = -3 \cos t$

3. 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.