Ask question
Question

# Find (\partial w/\partial x)y,z if w=x^{2}+y-z+\sin t and x+y=t

Derivatives
ANSWERED
asked 2021-05-04

Find $$\displaystyle{\left(\partial\frac{{w}}{\partial}{x}\right)}{y},{z}$$ if $$\displaystyle{w}={x}^{{{2}}}+{y}-{z}+{\sin{{t}}}$$ and $$x+y=t$$

## Answers (1)

2021-05-05

Step 1
To find the partial derivatives.
Step 2
given that
$$\displaystyle{w}={x}^{{{2}}}+{y}-{z}+{\sin{{t}}}$$
$$x+y=t$$
now
$$\displaystyle{w}={x}^{{{2}}}+{y}−{z}+{\sin{{\left({x}+{y}\right)}}}$$
$$\displaystyle{\frac{{\partial{w}}}{{\partial{x}}}}={\frac{{\partial}}{{\partial{x}}}}{\left({x}^{{{2}}}+{y}-{x}+{\sin{{\left({x}+{y}\right)}}}\right)}$$
$$\displaystyle={2}{x}+{\cos{{\left({x}+{y}\right)}}}$$
$$\displaystyle{\frac{{\partial{w}}}{{\partial{y}}}}={\frac{{\partial}}{{\partial{y}}}}{\left({x}^{{{2}}}+{y}-{z}+{\sin{{\left({x}+{y}\right)}}}\right)}$$
$$\displaystyle={1}+{\cos{{\left({x}+{y}\right)}}}$$
$$\displaystyle{\frac{{\partial{w}}}{{\partial{z}}}}={\frac{{\partial}}{{\partial{z}}}}{\left({x}^{{{2}}}+{y}-{z}+{\sin{{\left({x},{y}\right)}}}\right)}$$
$$=-1$$

expert advice

...