Question

Find the derivatives of all orders of the functions y=\frac{x^{4}}{2}-(\frac{3}{2})x^{2}-x

Derivatives
ANSWERED
asked 2021-05-18
Find the derivatives of all orders of the functions \(\displaystyle{y}={\frac{{{x}^{{{4}}}}}{{{2}}}}-{\left({\frac{{{3}}}{{{2}}}}\right)}{x}^{{{2}}}-{x}\)

Answers (1)

2021-05-19
Step 1
Important point:
derivative of \(\displaystyle{x}^{{{n}}}={\frac{{{d}{\left({x}^{{{n}}}\right)}}}{{{\left.{d}{x}\right.}}}}={n}{x}^{{{\left({n}-{1}\right)}}}\)
Step 2
The functions \(\displaystyle{y}={\frac{{{x}^{{{4}}}}}{{{2}}}}-{\left({\frac{{{3}}}{{{2}}}}\right)}{x}^{{{2}}}-{x}\)
\(\displaystyle{y}'={\frac{{{4}{x}^{{{3}}}}}{{{2}}}}-{\left({\frac{{{3}}}{{{2}}}}\right)}{\left({2}{x}\right)}-{1}\)
\(\displaystyle{y}'={2}{x}^{{{3}}}-{3}\cdot{\frac{{{2}{x}}}{{{2}}}}-{1}\)
\(\displaystyle{y}'={2}{x}^{{{3}}}-{3}{x}-{1}\)
The derivatives of all orders of the functions y:
\(\displaystyle{y}'={2}{x}^{{{3}}}-{3}{x}-{1}\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...