Calculus - MultivariableCalculus - quiz2

Question 1: What is the partial derivative of $sin(xy) \frac{\partial}{\partial x}$

sin(xy) cos(xy) ycos(xy) y*sin(xy)

Question 2: What is the partial derivative of $cos(xy) \frac{\partial}{\partial y}$

xsin(xy) -xsin(xy) -sin(xy) cos(xy)

Question 3: What is the partial derivative of $x^2cos(xy) \frac{\partial}{\partial y}$

2xcos(xy) -2xsin(xy) -x^3sin(xy) 2xsin(xy)

Question 4: What is the partial derivative of $x^3sin(xy) \frac{\partial}{\partial x}$

3x^2sin(xy) x^3ycos(xy) 3x^2+x^3cos(xy) 3x^2sin(xy)+x^3ycos(xy)

Question 5: What is the partial derivative of $xyzcos(x+y) \frac{\partial}{\partial x}$

yzcos(x+y) cos(x+y)-xyzsin(x+y) yzsin(x+y) yzcos(x+y)-xyzsin(x+y)

Question 6: What is the partial derivative of $xy^2e^{xy}+x^2y^2 \frac{\partial}{\partial x}$

xy^3e^{xy}+2xy xy^3e^{xy}+y^2e^{xy}+2xy^2 y^2e^{xy}+2xy^2 xy^2e^{xy}+2xy^2

Question 7: What is the partial derivative of $x^{yz}$ $\frac{\partial}{\partial x}$

yzx^(yz-1) yzx^yz x^(yz-1) y*z*x^(yz)

Question 8: What is the partial derivate of $(3^y+3^z)^{yz}$ $\frac{\partial}{\partial x}$

1 yz(3^y+3^z)^(yz-1) 0 (3^y+3^z)^yz

Question 9: What is the partial derivative of (x^2+y^2)sin(x+y) $\frac{\partial}{\partial x}$

-cos(x+y)+2xsin(x+y) (x^2+y^2)cos(x+y)+2x -(x^2+y^2)cos(x+y)+2xsin(x+y) 2xsin(x+y)

Question 10: What is the partial derivative of $(xyz)^{xy}$ $\frac{\partial}{\partial z}$

(xyz)^xy xy(xyz)^(xy-1) xy*z^(xy-1) (x^2y^2z)^{xy-1}

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