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# Difference Between Simple Differentiation & Partial Differentiation.

I know the basic difference, I want to know where, when & under which condition partial differentiation is used 7 under which condition differentiation is used ?

What is the main criteria which is needed for partial differentiation ?

What is the main criteria which is needed for partial differentiation ?

Partial differentiation is used only if the variable is a function of more than to variables

Eg

A=F(x,y) Where X=F(t) and Y=F(t)

Then while differentiating A completely with respect to t we go for partial differentiation

DA/Dt= dA/dx*Dx/Dt+dA/dy*Dy/Dt

A=x^2+y^2

x=3t^2+1

y=6t

Now to find DA/Dt we need to partially differentiate A with respect to X and Y

But we must completely differentiate X and Y equations

dA/dx=2x

dA/dy=2y

Dx/Dt=6t

Dy/Dt=6

This implies

DA/Dt =2x*6t +2y*6

Instead of x and y we substitute the equations of x and y thus we get DA/Dt a complete differential solution

Eg

A=F(x,y) Where X=F(t) and Y=F(t)

Then while differentiating A completely with respect to t we go for partial differentiation

DA/Dt= dA/dx*Dx/Dt+dA/dy*Dy/Dt

A=x^2+y^2

x=3t^2+1

y=6t

Now to find DA/Dt we need to partially differentiate A with respect to X and Y

But we must completely differentiate X and Y equations

dA/dx=2x

dA/dy=2y

Dx/Dt=6t

Dy/Dt=6

This implies

DA/Dt =2x*6t +2y*6

Instead of x and y we substitute the equations of x and y thus we get DA/Dt a complete differential solution