Question

Find both first partial derivatives. f(x,y)=4x^{3}y-2

Derivatives
ANSWERED
asked 2021-05-09
Find both first partial derivatives. \(\displaystyle{f{{\left({x},{y}\right)}}}={4}{x}^{{{3}}}{y}-{2}\)

Answers (1)

2021-05-11
Step 1
Given, \(\displaystyle{f{{\left({x},{y}\right)}}}={4}{x}^{{{3}}}{y}-{2}\)
Step 2
Differentiation partially with respect to x,
\(\displaystyle{\frac{{\partial{f}}}{{\partial{x}}}}={\frac{{\partial}}{{\partial{x}}}}{\left({4}{x}^{{{3}}}{y}-{2}\right)}={y}{\frac{{\partial{f}}}{{\partial{x}}}}{\left({4}{x}^{{{3}}}\right)}={y}{\left({12}{x}^{{{2}}}\right)}={12}{x}^{{{2}}}{y}\)
Differentiation partially with respect to y,
\(\displaystyle{\frac{{\partial{f}}}{{\partial{y}}}}={\frac{{\partial}}{{\partial{y}}}}{\left({4}{x}^{{{3}}}{y}-{2}\right)}={4}{x}^{{{3}}}{\frac{{\partial}}{{\partial{y}}}}{\left({y}\right)}={4}{x}^{{{3}}}\)
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