Question

Find all first partial derivatives of the following function. f(x,y)=(4x-y^{2})^{\frac{3}{2}}

Derivatives
ANSWERED
asked 2021-02-22
Find all first partial derivatives of the following function.
\(\displaystyle{f{{\left({x},{y}\right)}}}={\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{3}}}{{{2}}}}}}\)

Answers (1)

2021-02-24
\(\displaystyle{f{{\left({x},{y}\right)}}}={\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{3}}}{{{2}}}}}}\)
–°alculating the first derivatives.
\(\displaystyle{\frac{{\partial{f}}}{{\partial{x}}}}={\frac{{{3}}}{{{2}}}}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}\times{4}\)
\(\displaystyle\Rightarrow{\frac{{\partial{f}}}{{\partial{x}}}}={6}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}\)
\(\displaystyle{\frac{{\partial{f}}}{{\partial{x}}}}={\frac{{{3}}}{{{2}}}}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}\times-{2}{y}\)
\(\displaystyle\Rightarrow{\frac{{\partial{f}}}{{\partial{x}}}}=-{3}{y}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}\)
0
 
Best answer

expert advice

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