welcome to ✨implicit differentiation✨

#apcalc #calculus #derivatives #implicitdifferentiation

[OSAS]

The reason why implicit differentiation works is because the chain rule works. Once you take the derivative of the outer function( )^2 then you have to multiply it by the derivative of the inner function(X)

The chain rule serves to find the derivative of compound functions.

Like f[g(x)]

dy/dx= f’[g(x)]•g’(x)


For instance:

f(x)=X^2. —-> dy/dx =2X
d/dx X^2= 2X

You use the power rule for the exponent and then you chain out the inside and multiply it by its derivative dx/dx which is equal to 1. So then 2X•1= 2X

[gabriellerenee]

I have watched so many videos on this and did not understand. You said it so simply it seems so clear now 😭 thank you

[forbiddenfursona]

I actually tried to use Chain Rule after doing Implicit Diff. out of curiosity and it WORKED 😭😭😭

it will end up as y = ( -x² + 25 ) ^ ( ½ )
then when derived:
y' = [ 2x ] / [ 2 ( -x² + 25 ) ^ ( ½ ) ]

then just substitute that weird thing in the denominator with the equation for y above, then it's:
y' = 2x / 2y

[mega-mspy]

Plz do one for Leibniz's notation

[be-mrtj]

I understand the method, but how can we say that d/dx(y)=dy/dx if y cannot be expressed as a function of x directly?