Calc 1 Review

Chian Rule

100

What is the derivative of (3x²+5)³?

18x(3x²+5)²

200

What is the derivative of sin(4x⁵)?

20x⁴cos(4x⁵)

300

What is the derivative of e^5x?

5e^5x

400

What is the derivative of ln(7x)?

1/x

500

What is the derivative of csc((6x⁴-12x³+5x^-2)^3/2)?

-csc((6x⁴-12x³+5x^-2)^3/2)cot((6x⁴-12x³+5x^-2)^3/2) 3/2(6x⁴-12x³+5x^-2)^1/2(24x³-36x²-10x^-3)

Power Rule

100

What is the derivative of x³-4

3x²

200

What is the derivative of (5/4)x² - 6x?

(5/2)x - 6

300

What is the derivative of 1/x²?

-2/x^-3

400

What is the derivative of x^7/3?

(7/3)x^4/3

500

What is the derivative of the cube root of x

(1/3)x^-2/3

Product Rule

100

What is the derivative of xcos(x)?

cos(x)-xsin(x)

200

What is the derivative of e^x3x²?

e^x3x²+e^x6x

300

What is the derivative of sec(x)tan(x)?

sec(x)tan²(x) + sec³(x)

400

What is the derivative of 5x^2/3ln(x)?

(10/3)x^-1/3ln(x) + 5x^-1/3

500

What is the derivative of e^4xtan(x)?

4e^4xtan(x) + e^4xsec²(x)

Limits

100

What is the limit as x approaches 2 of x^2 +5 equal to?

9

200

What is the limit as x approaches 5 of (x-5)/(x²-2x+15) equal to?

1/8

300

What is the limit as x approaches 4 of (x²-4x)/(x-square root of 4x) equal to?

8

400

What is the limit as x approaches infinity of x³/(x²+x) equal to? 

infinity

500

What is the limit as x approaches -infinity of (5^x-4)/3 equal to?

-4/3