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 3 years ago
In Leibniz notation, we have:
dy/dx = (dy/du)(du/dx)
Lets say we have the function
f(x) = (x^2 + 1)^1/2 < sqrt function
What is the du/dx part?
 3 years ago
In Leibniz notation, we have: dy/dx = (dy/du)(du/dx) Lets say we have the function f(x) = (x^2 + 1)^1/2 < sqrt function What is the du/dx part?

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giggles123
 3 years ago
Best ResponseYou've already chosen the best response.0The du/dx part tell you to differentiate the argument of your function. let u=sqrt(x) so you take the derivative of sqrt(x) and multiple it by the derivative of x. dy/dx of sqrt(x)=1/(2sqrtx)*du/dx(x^2+1)>(1/(2sqrt(x^2+1))*(2x)

dmancine
 3 years ago
Best ResponseYou've already chosen the best response.0Let u = x^2 + 1 Then f(u) = u^(1/2) \[\frac{d}{dx}f(x) = \frac{d}{du}f(u)\frac{d}{dx}u = \frac{d}{du}u^{1/2}\frac{d}{dx}(x^{2}+1)\]First part is\[\frac{d}{du}u^{1/2} = \frac{1}{2}u^{1/2}\]Second part is\[\frac{d}{dx}(x^2+1)=2x\]Now substitute back in for u, find the product, and simplify.
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