Question

If z=f(x,y), where x=2s+3t and y=3s-2t find d^2/ds^2, d^2/dsdt and d^2/dt^2 the d symbol is like charles rule i cant write it here.

Answer 1

So you want all of these partial derivatives of z? e.g.,
\[ \frac{\partial^2 z}{\partial s^2} \] ?

Answer 2

yes.

Answer 3

i dont know how to solve it.

Answer 4

Ok, well notice that the first derivative is by the chain rule
\[ \frac{\partial z}{\partial s} = \frac{\partial z}{\partial x}\frac{\partial x}{\partial s} +
\frac{\partial z}{\partial y}\frac{\partial y}{\partial s} \]
It's a pain to write out these partial derivatives all the time. So we introduce notation with subscripts, where the subscript variable is the one that is being differentiated. So this equation we can write as
\[ z_s = z_x x_s + z_y y_s \]

So far so good?

Answer 5

yes but what is z_s? i dont understant your sign.

Answer 6

\( z_s \) means the partial derivative of z with respect to s. That second equation is just a way to write the first equation; it's just faster to do it that way, because it's a pain--even here--to write out all of those partial derivative signs and fractions.

Answer 7

can you draw it how to solve it. it will be a big help

Answer 8

I'm getting to it, I just want to make sure you understand what I've written so far.

Now, given that \( x=2s+3t \) and \( y=3s-2t \), what are the partial derivatives \( x_s \) and \( y_s \)?

Answer 9

What is \[ x_s = \partial x / \partial s \]

Answer 10

i dont know shoul i set it in the formel?

Answer 11

Cmon, if x = 2s + 3t, you must know how to find
\[ \partial x / \partial s \] no?

Answer 12

if not, then before you can answer this problem, you're going to need to go back and revise the basics of partial derivatives. This question builds on those basics.

Answer 13

yes but i dont understand it on calculus it is difficult for me to understand it. thats why i need help before eksamen

Answer 14

Before the exam, yes. I recommend you back at week or so in your class notes, and/or go back a chapter in your book. Make sure you can work the earlier problems. Then when you've mastered the basics of partial differentiation, you will be ready to try this problem.

Answer 15

We're here to help, but it won't help you if I give you the complete solution to this problem, because you won't be able to follow the steps.

Answer 16

yes i will be able to do my eksamen if i follow the steps of this example. it will be easier for me to solve such a quistion