RULES OF DIFFERENTIATION

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RULES OF DIFFERENTIATION

Conflict is present everywhere in the world around us. We experience conflict on a daily basis, and it can be minor or major.

Conflict in a story is a struggle between opposing forces. Characters must act to confront those forces and there is where conflict is born. If there is nothing to overcome, there is no story. Conflict in a story creates and drives the plot forward.

4. SUM RULE

If f(x)=h(x) +- g(x) f'(x)=h'(x) +- g'(x)

f(x)= -3x^2 + 4x =1 f'(x)= -6x + 4

3. POWER RULE

In this type of conflict, a character must take on society itself, and not a single person. The character stands at odds with societal norms and realizes the necessity to work against these norms. This is an external conflict.

If y=f(x)=x^n y'(x)=f'(x)=nx^n-1

Give examples of man versus society conflict in a literary work.

f(x)=5x^3 f'(x)=(3)5x^3-1 f'(x)=15x^2

2. CONSTANT-MULTIPLE RULE

This situation results from a protagonist working against what has been foretold for that person. While this conflict was more prevalent in stories where gods could control fate, such as in ancient Greek dramas, there are still examples of this type of conflict in more contemporary literature.

If f(x)=mx , where m is any constant f'(x)=dy/dx=m

Give examples of man versus fate conflict in a literary work.

If f(x)=5x f'(x)=5

1. CONSTANT FUNCTION/RULE

A more contemporary type of conflict, this situation results from humans involved in a struggle with man-made machines. This is an external conflict.

if y=f(x)=c , where c is any constant dy/dx=f'(x)=0

Give examples of man versus machine conflict in a literary work.

If f(x)=4 f(x)=0

7. QUOTIENT/RATIONAL RULE

This conflict develops from a protagonist’s inner struggles and may depend on a character trying to decide between good and evil or overcoming self-doubt. This conflict has both internal and external aspects, as obstacles outside the protagonist's force them to deal with inner issues.

If y=h(x)/g(x) let h(x)=u , g(x)=v y'=dy/dx= (vu'-uv')/v^2

Give examples of man versus self conflict in the real world.

f(x)=3x/(2x+1) u' = 3 v' = 2 so ; f'(x)=[(2x+1)3 - 3x(2)] / (2x+1)^2 =(6x+3-6x) / (2x+1)^2 =3/(2x+1)^2

6. PRODUCT RULE

In this type of conflict, a character is tormented by natural forces such as storms or animals. This is also an external conflict.

If y=h(x) x g(x) let h(x)=u , g(x)=v y'=uv'+vu' =u(dv/dx) + v(du/dx)

Give examples of man versus nature conflict in the real world.

f(x)=(4x-5)(-2x^2 + 3) u' = 4 v' = -4x so ; f'(x) = uv' + vu' f'(x)=(4x-5)(-4x)+((-2x^2)+3)(4) = -16x^2 + 20x - 8x^2 + 12 = -24x^2 + 20x + 12

5. CHAIN RULE

A situation in which two characters have opposing desires or interests. The typical scenario is a conflict between the protagonist and antagonist. This is an external conflict.

If f(x)=(ax +- b)^n f'(x)= n(ax +- b)^n-1 (ax +- b)

Give examples of man versus man conflict in the real world.

f(x)=(3x-2)^5 f'(x)=5(3x-2)^4 (3x-2) f'(x)=5(3x-2)^4 (3) f'(x)=15(3x-2)^4