Simple Calculus Overview Part 1

These will be some of the topics that I will be

covering in this website.

This is just a simplified version of each one of these topics that I will be covering more in depth In a separate post.

Outline

definition of a derivative

Learning about derivatives

When your x term has a power you simply

bring it to the front and then you subtract one from the original power to gain your new power.

Power rule

f(x) = x² + 10 2x

f(x) = 3x ² + 5x 6x + 5

f(x) = 4x3 + 2x2 + x 12x2 + 4x + 1

Functions that you can use the power rule with

The derivative of a function where two terms

are being multiplied can be expressed as the function of the first term times the derivative of the next term plus the derivative of the first term times the function of the second term.

Product rule

f(x) = 2x + 3 g(x) = 4x + 5

(f ⋅ g)′ = ( 2x + 3)( 4) + (2)(4x +5) = (8x + 12) + (8x +10 ) = 16x + 22

Functions that you can use the Product rule with

The derivative of a function with terms that

are being divided can be expressed by the function of the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the denominator squared.

Quotient rule

((3x + 5) /(4x+ 2)) ′ = ((4x + 2)(3) – (3x +

5)(4))/(4x + 2)2

= 12x + 6 – (12x + 20) /(4x + 2)2

= -14/(4x + 2)2

Functions that you can use the quotient rule with

Calculus is fun