Confussed when it comes to showing equation in terms of an independent variable

[sinclairharry]

Question:

Find the following derivatives. Express your answer in terms of the independent variables.

z_s and z_t where z = 3 x y - 4 x^2 y, x= 4s + 3t and y = 4s - 3t

My answer for z_s is -16x^2 + x(12-32y) + 12y

i am told my derivative is correct yet i dont know how to put it in terms of s and t
could some please help cheers?

 

[Ishuda]

Question:

Find the following derivatives. Express your answer in terms of the independent variables.

z_s and z_t where z = 3 x y - 4 x^2 y, x= 4s + 3t and y = 4s - 3t

My answer for z_s is -16x^2 + x(12-32y) + 12y

i am told my derivative is correct yet i dont know how to put it in terms of s and t
could some please help cheers?

Possibly the easiest (but most tedious) way is to just substitute for x and y and work it out, for example 12y=48s-36t. Then do the simplification.

 

[Steven G]

Question:

Find the following derivatives. Express your answer in terms of the independent variables.

z_s and z_t where z = 3 x y - 4 x^2 y, x= 4s + 3t and y = 4s - 3t

My answer for z_s is -16x^2 + x(12-32y) + 12y

i am told my derivative is correct yet i dont know how to put it in terms of s and t
could some please help cheers?

I am concerned about what you think '=' means.

In -16x^2 + x(12-32y) + 12y why not just replace x with 4s+3t and y with 4s-3t?

 

[Steven G]

Question:

Find the following derivatives. Express your answer in terms of the independent variables.

z_s and z_t where z = 3 x y - 4 x^2 y, x= 4s + 3t and y = 4s - 3t

My answer for z_s is -16x^2 + x(12-32y) + 12y

i am told my derivative is correct yet i dont know how to put it in terms of s and t
could some please help cheers?

You can also sub 4s+3t for x and 4s-3t for y in z = 3 x y - 4 x^2 y and then calculate z_s and z_t