How do you use the chain rule to differentiate #y=root5(-x^3-4)#?

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Answer 1 · 2017-04-10T02:34:13

#dy/dx=(-3x^2)/(5(-x^3-4)^(-4/5)#

Rewrite the function as,

#y=(-x^3-4)^(1/5)#

The chain rule has a general forumla of,

#dy/dx=dy/(du)*(du)/(dx)#

Applying that rule,

#dy/dx=[(-x^3-4)^(-4/5)/(1/5)]*(-3x^2)#

Simplify,

#dy/dx=[(-x^3-4)^(-4/5)*(-3x^2)]/5#

Rewrite (eliminate the negative exponents),

#dy/dx=(-3x^2)/(5(-x^3-4)^(-4/5)#