Derivative Practice

Misc I

100

Find the result of tan (-pi/4)

What is -1?

200

Condense the expression 

5log_3(x) - log_3(8x)

log_3(x^4/8)

300

Complete the square for f(x)=2x^2+4x-3

f(x)=2(x+1)^2-5

400

Find the vertex of y= x²-5x-1.

What is (5/2, -29/4)?

500

Simplify the expression (1/(x+1))/(1/(x-1))

(x-1)/(x+1)

600

Simplify (2+\sqrt3)/(2-\sqrt5)

-9 - 2\sqrt3 - 2\sqrt5

Calculus (Quotient Rule)

100

Find the derivative of: y = 

(-3(3x - 2x^2))/(7x)

What is: y'= 

6/7

200

Find the derivative of : y= 

What is : y'=

(-5x^2 + 4x +5)/(x^2 +1)^2

300

Find the derivative of: y= 

(1 - cos x)/ sinx

What is: y'= csc²x - cscx cotx.   or

(1- cosx)/ sin^2 x

400

Find the derivative of:  y= 

(x^2)/(2sqrtx + 1

What is: y' = 

(x(3sqrtx + 2))/(2sqrtx + 1)

500

Find the slope of the tangent line at (4,7) to:

 f(x)= 

What is: 

-17/4

600

Find an equation of the tangent line at (-1,1) of the graph: f(x) = [3 - (1/x)]/ (x +5)

What is:  y= 1 ?

Calculus (Chain Rule)

100

y=sin(cosx)

-cos(cosx)sinx

200

f(t)=sqrt(1-t)

f'(t)=-1/(2(1-t)^1/2)

300

s(t)=1/(t^2+3t-1)

(-2t-3)/(t^2+3t-1)^2

400

y=(2x-7)^3

y'=6(2x-7)^2

500

y=sin(pi x)

y'=pi cos(pi x)

600

y=x^2e^x-2xe^x+2e^x

y'=x^2e^x

Calculus (Product Rule)

100

Find the derivative of:  y=(3x-2x²)(5 + 4x)

What is:  y' = -24x² +4x + 15.

200

Find the derivative of:  y= 3x²sin(4x).

What is: y'= 6x[sin(4x) + 2xcos(4x)]

300

Find the derivative of: y= sin x cos x

What is:  y'= cos²x - sin²x

400

Find the derivative of:  y = (x² +3)(5x⁴ -(1/x))

What is: y'=  30x⁵ + 60x³ + (3/x²) - 1

500

Find the derivative of: y= x²cos x, at c = pi/6.

What is: y' = 

(pi*sqrt3)/6 - pi^2/72

600

Find y'(2), if : y = (x - 4)(x² + 6x -1)

What is: -5

Calculus (Anything)

100

Find the derivative of f(x) = [ cos(2x) ]²

What is: -4[cos(2x)](sin(2x))

200

Find the derivative of f(x) = sin²(4x)

What is 8 sin (x) cos (x)?

300

Find the slope of f(x)= (5/x³) - 3(x²)- (1/x) at x = -1

What is -8?

400

Find the derivative of:  f(x)= y=sin(tan 2x)

What is :  2cos(tan 2x)(sec²(2x))

or

[2cos(tan 2x)]/(cos²(2x))

500

The slope of the normal line to the curve y= (2x²) + 1 at (1,3) is

What is -1/4 ?

600

Find the slope of the graph of f(x) at the given pt:

f(x)= 3cosx - 2x ,  (0,3)  

What is :   -2