How do you take the derivative of a multivariable function? How would the chain rule work?
say, add(x,y) == x+y
the derivative is 1 + dy/dx
but what of the chain rule?
Printable View
How do you take the derivative of a multivariable function? How would the chain rule work?
say, add(x,y) == x+y
the derivative is 1 + dy/dx
but what of the chain rule?
you'll have to be more specific. are you trying to find a partial derivative? are you looking for dy/dx , dx/dy, ....? taking a derivative of a multivariable function is kind of a general term.
Basically, for a function z=f(x,y) of two independent variables, to take the partial derivative of z with respect to either x or y, you hold the other one constant. The symbol isn't a 'd', but 'd' will suffice, so dz/dx=df(x,y)/dx.
You can generalize to directional derivatives however, where you choose some unit vector (in this case, in 2-space), and take the derivative in that direction (often by using cosines of angles).
Let x = x(t) and y = y(t) be differentiable at t and suppose that z = f(x, y) is differentiable at the point (x(t), y(t)). Then z = f(x(t), y(t)) is differentiable at t and: