Question

Find all first partial derivatives. f(x,y)=5x^3+7y-3

Derivatives
ANSWERED
asked 2021-02-25
Find all first partial derivatives. \(\displaystyle{f{{\left({x},{y}\right)}}}={5}{x}^{{3}}+{7}{y}-{3}\)

Answers (1)

2021-02-26
Step 1
Given:
First partial derivation, \(\displaystyle{f{{\left({x},{y}\right)}}}={5}{x}^{{3}}+{7}{y}-{3}\)
Find all first partial derivatives,
\(\displaystyle{f}_{{x}}=\frac{{\partial{f}}}{{\partial{x}}}\)
\(\displaystyle={15}{x}^{{2}}+{0}-{0}\)
\(\displaystyle={15}{x}^{{2}}\)
\(\displaystyle{f}_{{y}}=\frac{{\partial{f}}}{{\partial{y}}}\)
\(\displaystyle={0}+{7}-{0}={7}\)
Step 2
\(\displaystyle{f}_{{\times}}=\frac{\partial}{{\partial{x}}}{\left(\frac{{\partial{f}}}{{\partial{x}}}\right)}\)
\(\displaystyle=\frac{{\partial}}{{\partial{x}}}{\left({15}{x}^{{2}}\right)}={30}{x}\)
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