How do you use the chain rule to differentiate $y = {(5 x^{4} + 1)}^{2}$ $y=(5x^4+1)^2$ ?

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How do you use the chain rule to differentiate $y = {(5 x^{4} + 1)}^{2}$ $y=(5x^4+1)^2$ ?

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Answer 1 · 2017-05-01T18:07:57

$\frac{d y}{d x} = 200 x^{7} + 40 x^{3}$ $dy/dx=200x^7+40x^3$

Explanation:

$d/dx(f(g(x)))=f'(g(x))xxg'(x)larr" chain rule"$

$"here "f(g(x))=(5x^4+1)^2$

$g(x)=5x^4+1$

$y=(5x^4+1)^2$

$rArrdy/dx=2(5x^4+1)xxd/dx(5x^4+1)$

$color(white)(rArrdy/dx)=2(5x^4+1)xx20x^3$

$color(white)(rArrdy/dx)=40x^3(5x^4+1)$

$color(white)(rArrdy/dx)=200x^7+40x^3$

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How do you use the chain rule to differentiate $y = {(5 x^{4} + 1)}^{2}$ $y=(5x^4+1)^2$ ?

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Science

Math

Humanities

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How do you use the chain rule to differentiate y=(5x^4+1)^2y=(5x4+1)2y=(5x^4+1)^2?

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Explanation:

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How do you use the chain rule to differentiate $y = {(5 x^{4} + 1)}^{2}$ $y=(5x^4+1)^2$ ?