Question

Find derivatives for the functions. Assume a, b, c, and k are constants. g(x)=\frac{x^{2]+\sqrt{x}+1}{x^{\frac{3}{2}}}

Derivatives
ANSWERED
asked 2021-06-06
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+\sqrt{{{x}}}+{1}}}{{{x}^{{{\frac{{{3}}}{{{2}}}}}}}}}\)

Expert Answers (1)

2021-06-07
First simplify g(x)
\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+\sqrt{{{x}}}+{1}}}{{{x}^{{{\frac{{{3}}}{{{2}}}}}}}}}={x}^{{{\frac{{{1}}}{{{2}}}}}}+{x}^{{-{1}}}+{x}^{{{\frac{{-{3}}}{{{2}}}}}}\)
now use the power rule to get
\(\displaystyle{g}'{\left({x}\right)}={\frac{{{1}}}{{{2}}}}{x}^{{{\frac{{-{1}}}{{{2}}}}}}-{x}^{{-{2}}}-{\frac{{{3}}}{{{2}}}}{x}^{{{\frac{{-{5}}}{{{2}}}}}}\)
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