Question

Find the first partial derivatives. z=x^{5}-7y

Derivatives
ANSWERED
asked 2021-02-20
Find the first partial derivatives.
\(\displaystyle{z}={x}^{{{5}}}-{7}{y}\)

Answers (1)

2021-02-22
Step 1
We have to find the first partial derivatives of \(\displaystyle{z}={x}^{{{5}}}-{7}{y}\)
Step 2
Now, \(\displaystyle{\frac{{\partial{z}}}{{\partial{x}}}}={\frac{{\partial}}{{\partial{x}}}}{\left({x}^{{{5}}}-{7}{y}\right)}\)
\(\displaystyle\Rightarrow{\frac{{\partial{z}}}{{\partial{x}}}}={5}{x}^{{{4}}}-{0}\)
\(\displaystyle\Rightarrow{\frac{{\partial{z}}}{{\partial{x}}}}={5}{x}^{{{4}}}\)
And
\(\displaystyle{\frac{{\partial{z}}}{{\partial{y}}}}={\frac{{\partial}}{{\partial{y}}}}{\left({x}^{{{5}}}-{7}{y}\right)}\)
\(\displaystyle{\frac{{\partial{z}}}{{\partial{y}}}}={0}-{7}=-{7}\)
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