Calculus - MultivariableCalculus - quiz2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Back to Quizzes