# How does implicit differentiation work?

Implicit differentiation is a way of differentiating when you have a function in terms of both x and y. For example:

#x^2+y^2=16#

This is the formula for a circle with a centre at (0,0) and a radius of 4

So using normal differentiation rules

#d/dx(x^2)+d/dx(y^2)=d/dx(16)#

#2x+d/dx(y^2)=0#

To find

#d/dx=d/dy *dy/dx#

#d/dy(y^2)=2y*dy/dx#

#2x+2y*dy/dx=0#

Rearrange for

#dy/dx=(-2x)/(2y#

#dy/dx=-x/y#

So essentially to use implicit differentiation you treat y the same as an x and when you differentiate it you multiply be

Youtube Implicit Differentiation

Theres another video on the subject here

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Implicit differentiation is a technique used to find the derivative of functions that are not explicitly expressed in terms of one variable. It involves differentiating both sides of an equation with respect to the variable of interest, treating the dependent variable as a function of the independent variable. This allows for the calculation of derivatives of functions where the dependent variable is not isolated explicitly.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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