Find derivatives for the functions. Assume a, b, c, and k are constants. y=\frac{x^{2}+2}{3}^{2}

Joni Kenny 2021-06-16 Answered
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{y}={\frac{{{x}^{{{2}}}+{2}}}{{{3}}}}^{{{2}}}\)

Want to know more about Derivatives?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Roosevelt Houghton
Answered 2021-06-17 Author has 17650 answers
Rewtire y
\(\displaystyle{y}={\left({\frac{{{x}^{{{2}}}+{2}}}{{{3}}}}\right)}^{{{2}}}={3}^{{-{2}}}{\left({x}^{{{2}}}+{2}\right)}^{{{2}}}\)
then
\(\displaystyle{y}'={\left[{3}^{{-{2}}}{\left({x}^{{{2}}}+{2}\right)}^{{{2}}}\right]}'\)
\(\displaystyle={3}^{{-{2}}}{\left({x}^{{{2}}}+{2}\right)}'\dot{{2}}{\left({x}^{{{2}}}+{2}\right)}\) Chain rule
\(\displaystyle={\frac{{{4}{x}{\left({x}^{{{2}}}+{2}\right)}}}{{{9}}}}\)
Not exactly what you’re looking for?
Ask My Question
47
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...