Solve using basic differentiation rule
y = 2/(x ^ (1/2)) + 6/(x ^ (1/3)) - 2/(x ^ (3/2)) + 4/(x ^ (3/4))
y=2x1/2+6x1/3−2x3/2+4x3/4=2x−1/2+6x−1/3−2x−3/2+4x−3/4y=\frac{2}{x^{1/2}}+\frac{6}{x^{1/3}}-\frac{2}{x^{3/2}}+\frac{4}{x^{3/4}}=2x^{-1/2}+6x^{-1/3}-2x^{-3/2}+4x^{-3/4}y=x1/22+x1/36−x3/22+x3/44=2x−1/2+6x−1/3−2x−3/2+4x−3/4
y′=−x−3/2−2x−4/3+3x−5/2−3x−7/4=−1x3/2−2x4/3+3x5/2−3x7/4y'=-x^{-3/2}-2x^{-4/3}+3x^{-5/2}-3x^{-7/4}=-\frac{1}{x^{3/2}}-\frac{2}{x^{4/3}}+\frac{3}{x^{5/2}}-\frac{3}{x^{7/4}}y′=−x−3/2−2x−4/3+3x−5/2−3x−7/4=−x3/21−x4/32+x5/23−x7/43
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