Question

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

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

$$\displaystyle{f{{\left({x},{y}\right)}}}={\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{3}}}{{{2}}}}}}$$
$$\displaystyle{\frac{{\partial{f}}}{{\partial{x}}}}={\frac{{{3}}}{{{2}}}}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}\times{4}$$
$$\displaystyle\Rightarrow{\frac{{\partial{f}}}{{\partial{x}}}}={6}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}$$
$$\displaystyle{\frac{{\partial{f}}}{{\partial{x}}}}={\frac{{{3}}}{{{2}}}}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}\times-{2}{y}$$
$$\displaystyle\Rightarrow{\frac{{\partial{f}}}{{\partial{x}}}}=-{3}{y}{\left({4}{x}-{y}^{{{2}}}\right)}^{{{\frac{{{1}}}{{{2}}}}}}$$