Question

If z = 3y^2 + 4 and y = 2x - 1 find dz/dx
With step by step explanation if you can

Answer 1

if
\[z(y)=3y^2+4, y(x) = 2x-1\] then by the "chain of relations"
\[z(x)=3(2x-1)^2+4\]

Answer 2

Z = 3(2x-1)(2x-1) +4
Z = 3(2x^2-4x+1) + 4
Z = 6x^2 - 12x + 7
taking the derivative of that you get
12x -12 = dz/dx

Answer 3

and by the "chain rule"
\[\frac{dz}{dx}=\frac{dz}{dy}\times \frac{dy}{dx}=6y\times 2=12y=12(2x-1)=24x-12\]

Answer 4

ha, 3 different answers! ok I think Sat is right though...
(dz/dx)=(dz/dy)(dy/dx)
chain rule
dy/dx=2
dz/dy=6y
(dz/dx)=12y=12(2x-1)=21x-12
Yes it seems Satellite is correct.

Answer 5

You cant just evaluate x into y and then take the derivative? why do you need the chain rule?

Answer 6

@cake4u i think we all have the same answer, and because this is a simple enough polynomial you don't need the chain rule, you can just multiply out as bensa did. but you wouldn't want to do that if you had, for example
\[z=y^{10}+y^6, y = 2x+1\]

Answer 7

Thanks alot for the input every1 :)