Derivative with Nested Square Roots f(x) = sqrt(4 + sqrt(6 + sqrt(x)))

Derivative with Nested Square Roots f(x) = sqrt(4 + sqrt(6 + sqrt(x)))

[sineup-]

another way you could have done it. is by implicit differentiation y=(4+(6+(x))^1/2)^1/2 then squaring both sides, y^2=4+(6+x^1/2)^1/2 then differentiating to 2ydy/dx=1/2(6+x^1/2)^-1/2 (1/2(x)^1/2) then dividing by 2y. dy/dx= 1/(4y(6+x^1/2)^1/2) then substituting y= (4+(6+(x))^1/2)^1/2 back in getting, as x^1/2 times (6+x^1/2)^1/2 =(6x+x(x)^1/2)^1/2 thanks loved the video it's so nice, the way you interact with your students.

[bryandavid]

What sorcery is this? It's too helpful, thank you so much sir!

[shahinjahanlu]

First every side power 2 then derivative