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

1 Answer

Oct 2, 2016

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

Explanation:

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)#

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