How do you find the derivative of #f(x)=sqrtx-5root3(x)#?

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Answer 1 · 2017-04-01T16:35:54

#f'(x) = frac{1-15x}{2sqrt{x}}.#

Using the sum rule, each term can be derived separately.

Changing the surds into indices makes f(x) easier to differentiate:

#f(x) = x^{1/2} - 5*x^{3/2}.#

Using the sum rule, each term can be derived separately:

#f'(x) = (1/2) * x^(-1/2) - 5*(3/2)*x^(1/2).#

#f'(x) = (1/2) * x^(-1/2) - (15/2)*x^(1/2).#

#f'(x) = frac{1-15x}{2sqrt{x}}#