Jones Test 3 Review

Chained Together

100

Differentiate:

 f(x) = csc(7x)

What is 

f'(x) = -7 csc(7x) cot(7x)

200

Derive y = sin²(4x-1)

What is 8 sin(4x-1) cos(4x-1)?

300

Differentiate:

f(x) = sin(3x² + x)

What is 

f'(x) = (6x + 1) cos(3x² + x) ?

400

Differentiate:

g(x) = ln(x^-4 + x⁴ )

What is 

g'(x) = (-4x^-5 + 4x³) / (x^-4 + x⁴) ?

500

Differentiate:

h(x) = tan(4 + 10x)

What is 

h'(x) = 10 sec² (4 + 10x)

Quotienting Products

100

Derive f(x) = 6x² / (2-x)

What is f'(x) = (24x-6x²) / (2-x)²

200

Derive f(x) = (3x + 9) / (2 - x)

What is 15 / (2-x)²?

300

Use Product Rule to find the derivative:

f(x) = (4x² - x) (x³ - 8x² + 12)

What is 20x⁴ - 132x³ + 24x² + 96x - 12?

400

Differentiate: 

R(t) = 1 / ( 2sin(t) - 4cos(t) ) 

What is 

R'(t) = ( -2cos(t) - 4sin(t) ) / ( 2sin(t) - 4cos(t) )² ?

500

Differentiate f(x) = (1+5x) / ln(x)

What is 

f'(x) = (5 ln(x) - 1/x - 5) / (ln(x))² ?

Triple Trig Trouble

100

Derive y(x)= csc(x) tan(x)

What is y'(x)= sec(x) tan(x)?

200

Differentiate the function: 

f(x) = 10tan(x) - 2cot(x)

What is 10sec²(x) + 2csc²(x)?

300

Evaluate lim_{x -> 0}  sin(10x)/ x

What is 10?

400

Differentiate h(t) = t³ - t² sin(t)

What is 

h'(t) = 3t² - 2t sin(t) - t²cos(t)?

500

Use implicit differential to find the derivative

tan^-1y=ln(x)

What is 

dy/dx = (1+y²) / x

Exponentially Cooked

100

Differentiate:

f(x) = 2e^x - 8^x

What is 

f'(x) = 2e^x - 8^xln(8) ?

200

Differentiate:

f(x) = 3e^x + 10x³ ln(x)

What is 

f'(x) = 3e^x + 30x² ln(x) + 10x²?

300

Differentiate:

y= 5e^x / (3e^x+1)

What is 

y' = 5e^x / (3e^x+1)² ?

400

Differentiate:

y = x⁵ - e^x ln(x)

What is

y' = 5x⁴ - e^x ln(x) - (e^x / x)

500

Differentiate: 

h(x) = x / (1-e^x) 

What is 

h'(x) = (1 - e^x + xe^x) / (1 - e^x)² ?

Inversed desrevnI

100

Evaluate cos^-1( - √2 / 2 )

What is y = 3π / 4 ?

200

Differentiate

T(x) = 2cos(x) + 6cos^-1(x)

What is 

T'(x) = -2sin(x) - 6 / √(1-x²) 

300

Differentiate: 

y= √x sin^-1(x)

What is 

y' = (1/2) x^-1/2 sin^-1(x) + ( √x / √(1-x²) )

400

Differentiate:

f(w) = sin(x) + x²tan^-1(x)

What is 

f'(x) = cos(x) + 2x tan^-1(x) + (x² / (1+x²) )

500

Differentiate: 

h(x) =  tan^-1(x) + 4cos^-1(x)

What is 

h'(x) = 1/ (1+x²) - ( 4 / sqrt (1-x²))