2.4-2.6 TEST

Find dy/dx for x² + xy = 10 when x = 2

• -7/2

• -2

• 2/7

• 3/2

What is the derivative of

 $\cos^2\left(x^3\right)?$  

•  $6x^2\sin\left(x^3\right)\cos\left(x^3\right)$  

•  $6x^2\cos\left(x^3\right)$  

•  $\sin^2\left(x^3\right)$  

•  $-6x^2\sin\left(x^3\right)\cos\left(x^3\right)$  

Find dy/dx for the following:

 $x^3+3xy+2y^3=17$  

•  $-\frac{x^2+y}{x+2y^2}$  

•  $-\frac{x^2+y}{x+y^2}$  

•  $\frac{x^2+y}{x+2y}$  

•  $\frac{-x^2}{1+2y^2}$  

 $\ f\left(x\right)=\left(x-1\right)^2\sin\left(x\right)$  
Find  $f'\left(0\right)$  

• -2

• -1

• 0

• 1

 $f\left(x\right)=\left(2x-1\right)^5\left(x+1\right)$  

Given the function above, which of the following is an equation for the line tangent to the graph at the point where x = 1? (Remember, you need a point and a slope to write the equation)

•  $y=21x+2$  

•  $y=21x-19$  

•  $y=11x-9$  

•  $y=10x+2$  

 $x^2y-3x=y^3-3$  

What is dy/dx at the point (-1,2) ?

• -7/11

• -7/13

• -1/2

• -3/14

 $x\cos\left(y\right)=1\$  

Find dy/dx for the relation above at the point  $\left(2,\ \frac{\pi}{3}\right)$  

•  $\frac{1}{2\sqrt{3}}$  

•  $2\sqrt{3}$  

•  $-\frac{1}{2\sqrt{3}}$  

•  $\frac{1}{2}$  

 $f\left(x\right)=3x^4\left(5x^2+1\right)^9$  

Derive the above function and FACTOR YOUR ANSWER COMPLETELY.

•  $6x^3\left(5x^2+1\right)^8\left(55x^2+2\right)$  

•  $6x^3\left(5x^2+1\right)^8\left(50x^2+1\right)$  

•  $4x^3\left(5x^2+1\right)^9\left(45x^2+2\right)$  

 $f\left(x\right)=\left(\frac{6x^2-1}{2x+2}\right)^5$  

Derive the function above. Your answer needs to be in the form of ONE FRACTION.

•  $\frac{5\left(6x^2-1\right)^4\left(12x^2+24x+2\right)}{\left(2x+2\right)^6}$  

•  $\frac{5\left(6x^2-1\right)\left(12x^2+24x+2\right)}{\left(2x+2\right)^6}$  

•  $\frac{5\left(6x^2-1\right)^4\left(12x^2+24x+2\right)}{\left(2x+2\right)^8}$  

Derive the following:  $f\left(x\right)=\sin4x^2\cos3x$  

•  $-3\sin4x^2\sin3x+8x\cos3x\cos4x^2$  

•  $3\sin4x^2\sin3x+8x\cos3x\cos4x^2$  

•  $8x\cos4x^2-3\sin3x$  

•  $-24x\cos4x^2\sin3x$