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This answer is incorrect. The denominator of the second step should be multiplied by \(2 [1/(2*\sqrt{x^2+1})]\).

This would cancel out the 2 in the numerator of the second part of the answer, leaving on \(x^3\) in the numerator.

Question

asked 2021-06-12

Find derivatives for the functions. Assume a, b, c, and k are constants.

\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}^{{{2}}}}}}+{5}\sqrt{{{x}}}-{7}\)

\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}^{{{2}}}}}}+{5}\sqrt{{{x}}}-{7}\)

asked 2021-06-06

Find derivatives for the functions. Assume a, b, c, and k are constants.

\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+\sqrt{{{x}}}+{1}}}{{{x}^{{{\frac{{{3}}}{{{2}}}}}}}}}\)

\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+\sqrt{{{x}}}+{1}}}{{{x}^{{{\frac{{{3}}}{{{2}}}}}}}}}\)

asked 2021-06-08

Find derivatives for the functions. Assume a, b, c, and k are constants.

\(\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{\sqrt{{{z}}}}}}\)

\(\displaystyle{f{{\left({z}\right)}}}={\frac{{{z}^{{{2}}}+{1}}}{{\sqrt{{{z}}}}}}\)

asked 2021-05-01

Find derivatives for the functions. Assume a, b, c, and k are constants.

\(\displaystyle{h}{\left({x}\right)}=\sqrt{{{\frac{{{x}^{{{2}}}+{9}}}{{{x}+{3}}}}}}\)

\(\displaystyle{h}{\left({x}\right)}=\sqrt{{{\frac{{{x}^{{{2}}}+{9}}}{{{x}+{3}}}}}}\)