Question

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

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

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
$$\displaystyle{\frac{{\partial{z}}}{{\partial{y}}}}={\frac{{\partial}}{{\partial{y}}}}{\left({x}^{{{5}}}-{7}{y}\right)}$$
$$\displaystyle{\frac{{\partial{z}}}{{\partial{y}}}}={0}-{7}=-{7}$$