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For the given composite function, identify the inner function, u \(y = \sqrt[3]{1 + 5x}\) \((f(u), g(x)) = (\tan u \pi x)\) Find the derivative \(\frac{dy}{dx}\). \(\frac{dy}{dx} = \frac{5}{3(1 + 5x)^{\frac{2}{3}}}\) Need Help? Read It Watch It 

          For the given composite function, identify the inner function, u
\(y = \sqrt[3]{1 + 5x}\)
\((f(u), g(x)) = (\tan u \pi x)\)
Find the derivative \(\frac{dy}{dx}\).
\(\frac{dy}{dx} = \frac{5}{3(1 + 5x)^{\frac{2}{3}}}\)
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For the given composite function, identify the inner function, u y = √(1 + 5x) (f(u), g(x)) = (tan u π x) Find the derivative (dy)/(dx). (dy)/(dx) = (5)/(3(1 + 5x)^(2)/(3)) Need Help? Read It Watch It

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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For the given composite function,identify the inner function, u y=1+5x fu,gx= tan unx dy Find the derivative dx 5 318 Need Help? Watch It
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Transcript

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00:03 We had the function, y equals 2x q plus 5 all raised to the fourth.
00:10 And ultimately we want to find d, y, d, x using the chain rule.
00:16 And so we want to write this function.
00:21 We want to write this function y as a function of u, where u itself is a function of x.
00:32 You can think of u equal some function g of x.
00:36 Without making it extra complicated, we simply just have to say u, okay, is going to be 2x cubed plus 5.
00:49 So that means y is equal to u to the fourth.
00:57 So we successfully wrote y as a function of u, y is equal to u to the fourth, where u itself is a function of x, okay, u equals 2x cubed plus 5.
01:14 So now, now we wish to find d, y, d, x.
01:28 Well, since y is the function of u and u is a function of x, using the chain rule, dy, dx is the derivative of y with respect to u, times the derivative of u with respect to x.
01:46 So let's go off to the side here, if y equals u to the fourth, dy, d, y, d, u is the derivative of u to the fourth with respect to you...
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