# Math 1251 Practice Gateway Exams

Practice Exam #1

1. The equation of the tangent line to the curve y=x^3-x at the point (2,6) is

2. If f(x)= x^2/(1-x), then f'(x)=?

3. If y= sin(x/2)*cos(3x), then dy/dx= ?

4. If f(x)= \sqrt(1+sin(2x)), then f'(x)=?

Practice Exam #2

1. If y=x*sin(3x), then dy/dx=?

2. The equation of the tangent line to the curve y=x/(1+x) at (1,1/2) is

3. If y=(1+x^4)^(1/2), dy/dx=?

4. If y= x+2/x then dy/dx=?

Practice Exam #3

1. If w=7t^3-1/t then dw/dt=?

2. If f(x)=sin(3-2x) then f'(x)=?

3. If y=sin(x)*(x-cos(x)) then dy/dx=?

4. The equation of the tangent line to curve y=1/\sqrt(x) at (4,1/2) is

Practice Exam #4

1. The derivative if e^{x-4x^2} is

2. If y=1/cos(x), then dy/dx=?

3. If f(x)=(x-6)/(x+x^3), then f'(x)=

4. The equation of the tangent line to the curve y=e^x at (1,e) is

Practice Exam #5

1. If y=x*\sqrt(x-x^3), then dy/dx=?

2. The equation of the tangent line to the graph y=x^3+x at (2,10) is

3. If f(x)=sin(2+e^x) then f'(x)=?

4. If f(x)=x/(1+x) then f'(x)=?

Practice Exam #6

1. If y=x*sin(x^2), then dy/dx=?

2. If g(x)=x^6+3/x, then g'(x)=?

3. If y=e^x*cos(x/2) then dy/dx=?

4. If y=1/x, the equation of the tangent line to the graph of at (1,1) is

Practice Exam #7

1. If y=(x+2)/(sin(x)-x), then dy/dx=?

2. If y=\sqrt(x+1)*x, then dy/dx=?

3. If f(x)=(9-11x)^23, then f'(x)=?

4. The equation of the tangent line to the graph of y=cos(x) at (pi/4,1/\sqrt(2)) is

Practice Exam #8

1. The derivative of (4x-x^2)^6 is

2. If f(x)=(2-x)/x^2 then f'(x)=?

3. If y=sin(1-3x) then dy/dx=?

4. The equation of the tangent line to the y=(2x-1)^10 at (1,1) is

Practice Exam #9

1.The derivative of sin(2x)/cos(3x) is

2. If f(x)= (x^3+1)*(x^2+x) then f'(x)=?

3. If y=(1+cos(x))^25 then dy/dx=?

4. The equation of the tangent line to the graph of y=1/\sqrt(x) at (1,1) is

Practice Exam #10

1. The equation of the tangent line to the graph of y=\sqrt(4-x^2) at (-1,\sqrt(3)) is

2. If f(x)=x*(2x+1)^67, then f'(x)=?

3. If y= sin(3-9x) then dy/dx=?

4. If f(x)=x/\sqrt(1+x^2), then f'(x)=?

Practice Exam #11

1. If y^2+x*y=2, the equation of the tangent line to the curve y at (1,1) is

2. If y=x/cos(x), then dy/dx=?

3. If f(x)=\sqrt(1-x^7), then f'(x)=?

4. If y=sin(x^7-4x), then dy/dx=?

Practice Exam #12

1. If f(x)=(x^2+cos(x))^(4/3) then dy/dx=?

2. If y=sin(7-5x), then dy/dx=?

3. The equation of the tangent line to the curve y=2/y+x*y at (1,2) is

4. If y= cos(x/2)*x then dy/dx=?

Practice Exam #13

1. If f(x)=x*e^(-x^2), then f'(x)=?

2. If f(x)=sin(1-x^2)/x, then f'(x)=?

3. If y=(x^6-x^9+cos(2x))^11, then dy/dx=?

4. The equation of the tangent line to y=x-2x^2 at (1,-1) is

Practice Exam #14

1. If y=\sqrt(x-cos(x)), then dy/dx=?

2. If g(x)=(e^(2x)-x)^23, then g'(x)=?

3. If f(x)=cos(2x)/cos(x), then f'(x)=?

4. The equation of the tangent line to the curve y=1/x+1/x^2 at (1,2) is

Practice Exam #15

1. If y=log(x^2+e^x), dy/dx=?

2. If f(x)=x*(1+cos(2x)), f'(x)=?

3. The equation of the tangent line to the curve y=(2x+1)^25 at (0,1) is

4. If y=\sqrt(x^2-4x^4), then dy/dx=?