Calculate $\frac { \partial f } { \partial x }$ , and $\frac { \partial f } { \partial y }$ when defined. $f ( x , y ) = 9 x ^ { 0.7 } y ^ { 0.9 }$
A) $\frac { \partial f } { \partial x } = 6.3 x ^ { 1.7 } y ^ { 0.9 }$ , $\frac { \partial f } { \partial y } = 8.1 x ^ { 0.7 } y ^ { 1.9 }$
B) $\frac { \partial f } { \partial x } = - 6.3 x ^ { - 0.3 } y ^ { 0.1 }$ , $\frac { \partial f } { \partial y } = - 8.1 x ^ { 0.3 } y ^ { - 0.1 }$
C) $\frac { \partial f } { \partial x } = 6.3 x ^ { - 0.3 }$ , $\frac { \partial f } { \partial y } = 8.1 y ^ { - 0.1 }$
D) $\frac { \partial f } { \partial x } = 6.3 x ^ { - 0.3 } y ^ { 0.9 }$ , $\frac { \partial f } { \partial y } = 8.1 x ^ { 0.7 } y ^ { - 0.1 }$
E) $\frac { \partial f } { \partial x } = 6.3 x ^ { - 0.3 } y ^ { 0.9 }$ , $\frac { \partial f } { \partial y } = 8.1 x ^ { 1.7 } y ^ { - 1.9 }$

Question

Calculate $\frac { \partial f } { \partial x }$ , and $\frac { \partial f } { \partial y }$ when defined.   $f ( x , y ) = 9 x ^ { 0.7 } y ^ { 0.9 }$  
A) $\frac { \partial f } { \partial x } = 6.3 x ^ { 1.7 } y ^ { 0.9 }$ , $\frac { \partial f } { \partial y } = 8.1 x ^ { 0.7 } y ^ { 1.9 }$
B) $\frac { \partial f } { \partial x } = - 6.3 x ^ { - 0.3 } y ^ { 0.1 }$ , $\frac { \partial f } { \partial y } = - 8.1 x ^ { 0.3 } y ^ { - 0.1 }$
C) $\frac { \partial f } { \partial x } = 6.3 x ^ { - 0.3 }$ , $\frac { \partial f } { \partial y } = 8.1 y ^ { - 0.1 }$
D) $\frac { \partial f } { \partial x } = 6.3 x ^ { - 0.3 } y ^ { 0.9 }$ , $\frac { \partial f } { \partial y } = 8.1 x ^ { 0.7 } y ^ { - 0.1 }$
E) $\frac { \partial f } { \partial x } = 6.3 x ^ { - 0.3 } y ^ { 0.9 }$ , $\frac { \partial f } { \partial y } = 8.1 x ^ { 1.7 } y ^ { - 1.9 }$

Quizplus · Accepted Answer

To find the partial derivatives, apply the power rule. For $\frac{\partial f}{\partial x}$, treat $y$ as a constant and differentiate $9x^{0.7}$ to get $6.3x^{-0.3}y^{0.9}$. For $\frac{\partial f}{\partial y}$, treat $x$ as a constant and differentiate $9y^{0.9}$ to get $8.1x^{0.7}y^{-0.1}$.

Calculate ∂f∂x\frac { \partial f } { \partial x }∂x∂f​ , And

Calculate $\frac { \partial f } { \partial x }$ , And