# Write formulas for the indicated partial derivatives for the multivariable function.f(x,y)=7x^2+9xy+4y^3a)(delf)/(delx)b)(delf)/(dely)c)(delf)/(delx)|_(y=9)

Write formulas for the indicated partial derivatives for the multivariable function.
$f\left(x,y\right)=7{x}^{2}+9xy+4{y}^{3}$
a)$\frac{\partial f}{\partial x}$
b) $\frac{\partial f}{\partial y}$
c)$\frac{\partial f}{\partial x}{\mid }_{y=9}$

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$f\left(x,y\right)=7{x}^{2}+9xy+4{y}^{3}$ (1)
a) Differentiating with respect to x partially, we have
$\frac{\partial f}{\partial x}=\frac{\partial }{\partial x}\left[7{x}^{2}+9xy+4{y}^{3}\right]$
$\frac{\partial f}{\partial x}=7\cdot 2x+9y+0$
$\frac{\partial f}{\partial x}=14x+9y$
b) Differentiating with respect to y partially, we have
$\frac{\partial f}{\partial y}=\frac{\partial }{\partial y}\left[7{x}^{2}+9xy+4{y}^{3}\right]$
$\frac{\partial f}{\partial y}=0+9x+4\cdot 3{y}^{2}$
$\frac{\partial f}{\partial y}=9x+12{y}^{2}$
c) $\frac{\partial f}{\partial x}{\mid }_{y=9}=14x+9\cdot 9$
$\frac{\partial f}{\partial x}{\mid }_{y=9}=14x+81$