Answer
$y'=-\dfrac{1}{2\sqrt{x^{3}}}+\dfrac{3}{5\sqrt[5]{x^{8}}}$
Work Step by Step
$y=\dfrac{1}{\sqrt{x}}-\dfrac{1}{\sqrt[5]{x^{3}}}$
Rewrite the denominators by expressing them as powers with rational exponents:
$y=\dfrac{1}{\sqrt{x}}-\dfrac{1}{\sqrt[5]{x^{3}}}=\dfrac{1}{x^{1/2}}-\dfrac{1}{x^{3/5}}=...$
Now, change the sign of the exponents of the denominators by taking them to the numerator:
$...=x^{-1/2}-x^{-3/5}$
Now, evaluate the derivate using the power rule:
$y'=-\dfrac{1}{2}x^{-1/2-1}-\Big(-\dfrac{3}{5}\Big)x^{-3/5-1}=...$
$...=-\dfrac{1}{2}x^{-3/2}+\dfrac{3}{5}x^{-8/5}=...$
Give the answer without negative exponents by taking the powers to the denominator and changing the sign of the exponents:
$...=-\dfrac{1}{2x^{3/2}}+\dfrac{3}{5x^{8/5}}=-\dfrac{1}{2\sqrt{x^{3}}}+\dfrac{3}{5\sqrt[5]{x^{8}}}$
