partial derivatives -quiz

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

Tags

CCSS.HSA.APR.A.1

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Tags

CCSS.HSA.APR.A.1

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Tags

CCSS.HSA.APR.A.1

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.TF.A.2

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Find the first order partial derivative with respect to y
 $f(x,y)=x^3y^2+3xe^y$  
.

•  ^{$f_y(x,y)=3x^2y^2+3e^y$}  

•  $f_y(x,y)=3x^2y^2+2x^3y+3e^y+3xe^y$  

•  $f_y(x,y)=2x^3y+3xe^y$  

•  $f_y(x,y)=6x^2+3e^y$  

Find the Partial derivative of f with respect to y for  $f\left(x,y\right)=\frac{y^2}{x+y}$  

•  $\frac{2x+y}{\left(x+y\right)^2}$  

•  $\frac{2xy+y^2}{\left(x+y\right)^2}$  

•  $\frac{2}{\left(x+y\right)^{ }}$  

•  $\frac{2x^2+y^2}{\left(x+y\right)^2}$  

 $Find\ \frac{\partial f}{\partial x}for\ f\left(x,y\right)=3e^{2x}+7xy-3x$  

•  $6e^{2x}+7y-3$  

•  $6e^{2x}+7x-3$  

•  $6e^x+7y-3$  

•  $6e^{2x}+7y+7x-3$  

Find  $\frac{\partial f}{\partial x}$  of  $f\left(x,y\right)=\sin\left(\frac{x}{1+y}\right)$  

•  $\cos\left(\frac{x}{1+y}\right)$  

•  $\cos\left(\frac{x}{1+y}\right)\left(\frac{1}{1+y}\right)$  

•  $-\cos\left(\frac{x}{1+y}\right)\left(\frac{x}{\left(1+y\right)^2}\right)$  

•  $\sin\left(\frac{x}{1+y}\right)\left(\frac{1}{1+y}\right)$  

 $\lim_{\left(x,y\right)\rightarrow\left(1,1\right)}\frac{\left(4x-5y\right)}{5x^2-7y}$ 

• Limit DNE

•  $\frac{1}{2}$  

•  $-\frac{1}{2}$  

• 2