How do you differentiate $f(x)=(x^3-5x)^4$ ?

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Answer 1 · 2016-10-02T01:14:37

Use the chain rule, $(df)/dx = (df)/(du)(du)/(dx)$

Let $u = x^3 - 5x$ , then, $f(u) = u^4$ , $(df)/(du) = 4u^3$ , and $(du)/(dx) = 3x² - 5$

Substituting this into the chain rule:

$(df)/dx = 4u³(3x² - 5)$

Reverse the u substitution:

$(df)/dx = 4(x^3 - 5x)³(3x² - 5)$

How do you differentiate f(x)=(x^3-5x)^4f(x)=(x^3-5x)^4?