How do you differentiate #f(x)= 5/x^3 - 3/ x^(1/3)#?

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Answer 1 · 2015-10-14T01:32:48

#f^'(x) = -15/x^4 + 1/x^(4/3)#

Put it on root notation

#f(x) = 5x^(-3) - 3x^(-1/3)#

Using the polynomial formula, #f^'(x) = nx^(n-1)#, we have

#f^'(x) = 5*(-3)* x^(-3-1) -3*(-1/3)*x^(-1/3-1)#

#f^'(x) = -15x^(-4) + x^(-4/3)#

Since the problem started with fraction notation, let us put the answer back in that notation

#f^'(x) = -15/x^4 + 1/x^(4/3)#