Which of the following statements are true?
1 answer:
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Answer:
Let z = f(x, y) where f(x, y) =0 then the implicit function is
Example:-
Step-by-step explanation:
<u>Partial differentiation</u>:-
- Let Z = f(x ,y) be a function of two variables x and y. Then
Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to x.
It is denoted by δ z / δ x or δ f / δ x
- Let Z = f(x ,y) be a function of two variables x and y. Then
Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to y
It is denoted by δ z / δ y or δ f / δ y
<u>Implicit function</u>:-
Let z = f(x, y) where f(x, y) =0 then the implicit function is
The total differential co-efficient
d z = δ z/δ x + δ z/δ y
<u>Implicit differentiation process</u>
- differentiate both sides of the equation with respective to 'x'
- move all d y/dx terms to the left side, and all other terms to the right side
- factor out d y / dx from the left side
- Solve for d y/dx , by dividing
Example :
solution:-
differentiate both sides of the equation with respective to 'x'
move all d y/dx terms to the left side, and all other terms to the right side
Taking common d y/dx