Question

26. If f(x,y) = 0, then the value of dy/
dx​

Answer 1

f(x,y) = 0

then dy / dx will be equal to 0

Differentiation of any constant function is always zero.

Answer 2

$\displaystyle \sf{ \frac{dy}{dx} = - \frac{ \dfrac{ \partial f}{\partial x} }{\dfrac{ \partial f}{\partial y}} }$

Given :

f(x,y) = 0

To find :

Find the value of dy/dx

Formula :

$\displaystyle \sf{ df = \dfrac{ \partial f}{\partial x}dx + \dfrac{ \partial f}{\partial y}dy }$

Solution :

Step 1 of 2 :

Write down the given function

Here the given function is f(x,y) = 0

Step 2 of 2 :

Find the value of dy/dx

f(x,y) = 0

Differentiating both sides we get

$\sf df = 0$

$\displaystyle \sf{ \implies \dfrac{ \partial f}{\partial x}dx + \dfrac{ \partial f}{\partial y}dy = 0}$

$\displaystyle \sf{ \implies \dfrac{ \partial f}{\partial y}dy = - \dfrac{ \partial f}{\partial x}dx}$

$\displaystyle \sf{ \implies \frac{dy}{dx} = - \frac{ \dfrac{ \partial f}{\partial x} }{\dfrac{ \partial f}{\partial y}} }$