Differential Calculus

Easy Questions

100

Give the notation or formula for antiderivative of  exponential function rule 1. 

Integral of e^x dx = e^x + c

200

Give the notation or formula for antiderivative of logarithmic function rule 1.

Integral of a^xdx = a^x / ln a + c

300

Give the notation or formula for antiderive of logarithmic function rule 4. 

 Integral of a^-1dx = Integral of 1/x dx = ln absolute value of x + c

400

What is the reciprocal of integral sinxdx in antiderivative of trigonometric function?

- cosx + c

500

What is the reciprocal of integral cscxcotxdx in antiderivative of trigonometric function?

- cscx + c

Derivatives

100

What is the derivative of  3x⁴ + 6x² -7?

12x³ + 12x

200

What is the derivative of 2x² using constant multiple rule.

4x

300

What is the derivative of x⁴ + 4x -5 using sum and difference rule.

4x³ + 4

400

What is the derivative of x² (x + 8) using constant product rule.

11x² + 16x

500

What is the derivative of y = x + 2 /  x² using quotient rule.

2x² + 3x + 2

BONUS QUESTIONS

100

What is the symbol used to describe an integral?

Integral sign

200

What are the two key part of Antiderivative?

Indefinite and Definite Integral

300

Give an example of Indefinite Integral 

 Integral of x² 

400

Give an example of definite integral.

Integral of x² from 1 to 5.

500

What is the symbol we used to denote a given derivatives?

d / dx or y'

Antiderivatives

100

Find the antiderivatives of 64x⁷ using constant multiple rule.

8x⁸ + c

200

Find the antiderivatives of integral x⁴ - 5x² + 2x - 5

x⁵/5 - 5 x³/3 + x² - 5x + c

300

Find the antiderivatives of 5x⁶ using power rule.

5x⁷ / 7 + c

400

Find the antiderivative of integral ( x⁴ + 5x²) using sum and difference rule.

x⁵ / 5 + 5x³ / 3 + c

500

Find the antiderivatives of integral x^-2

- 1/x + c

GENERAL KNOWLEDGE

100

What notation we used to describe an Antiderivative of a function?

F(x) or G(x), etc.

200

What do we call this rules when it comes to antiderivatives such as CONSTANT RULE, POWER RULE, CONSTANT MULTIPLE RULE and SUM AND DIFFERENCE RULE?

FOUR MAJOR THEOREMS

300

In solving ANTIDERIVATIVES OF A FUNCTION what do we call the rules we used?

ANTIDIFFERENTIATION RULES

400

In derivatives we accept the value of x⁰ as 1, except for?

BASE IS ZERO (0)

500

WHAT IS THE COMPLETE NAME OF YOUR BASIC CALCULUS TEACHER?

JACKYLOU SANTOS FERRY