What is the derivative of #Tan^-1 (y/x)#?
3 Answers
Explanation:
Using the chain rule on the left side:
Using the product rule on the right side:
Explanation:
This problem needs a slight prerequisite of chain rule, and quotient rule.
Thus,
It really depends upon what you are doing, and which independent variables matter to you.
Let
Using the Quotient Rule and Implicit Differentiation on
The partial derivatives are therefore:
#{(z_x = - y/(x^2 + y^2)),(z_y = x/(x^2 + y^2)):}#
But if
# dz/dx = ( x \ dy/dx - y \ dx/dx) /(x^2+y^2) #
Which is the total derivative wrt
# dz/dx = z_y dy/dx + z_x#