Question

use implicit differentiation to find dy/dx of (x^4+y^2)^(1/2)=5x+2y^3

Answer 1

please tell me how you arrived at your answer I can easily just find the answer in the back of my book what I don't know is how they got the answer

Answer 2

Is the book answer\[-\frac{2 x^3-5 \sqrt{x^4+y^2}}{y-6 y^2 \sqrt{x^4+y^2}} \]

Answer 3

yes. How did you arrive at that answer? I'm really having trouble understanding square root part of it

Answer 4

you have quotient derivative, just apply formula, when never the turn of y , take y' the sqr as a function . for example, if you have (x +4)^1/2 . take outer function first I mean take the ( ) as unique variable, take derivative of sqr = 1/2 (....) ^(1/2-1)* (....)'. you got it?

Answer 5

in principle i get it putting iI don't know if putting in practice would be as easy

Answer 6

btw thank you guys so much for replying to these questions I was worried. Majority of these questions aren't as difficult as the ones I'm asking.

Answer 7

I give you a simplest example to get that concept: \[(\sqrt{5x^2 +3})' = [(5x^2 +3)^1/2]' = \frac{ 1 }{2 }(5x^2+3)^(\frac{ 1 }{ 2 }-1) * (5x^2 +3)'\]

Answer 8

don't forget take derivative the last part to get the final answer. Step by step, you solve from out to in, outer layer is sqr, take it, then inner is exponent, take later

Answer 9

Alright that makes sense

Answer 10

@MATTW20
Take the total derivative of your expression, solve the result for dy and then divide both sides by dx. The following is the total derivative where Dt[a] is da.\[\frac{4 x^3 \text{Dt}[x]+2 y \text{Dt}[y]}{2 \sqrt{x^4+y^2}}= 5 \text{Dt}[x]+6 y^2 \text{Dt}[y]\]

Answer 11

I used Mathematica to perform the total derivative calculation.