Kategorier: Alle - chain - product - differentiation - power

af John Kelabu 4 år siden

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RULES OF DIFFERENTIATION

The document explains various rules of differentiation used in calculus. It covers the Quotient Rule, which is applied when differentiating a function that is the ratio of two other functions.

RULES OF DIFFERENTIATION

RULES OF DIFFERENTIATION

PECAHAN


6. Product Rule

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

4. Sum Rule

f'(x)=3x^2+3
Example : f(x)=x^3+3x
f'(x)=h'(x)+-g'(x)
If f(x)=h(x)+-g(x)

3. Power Rule

f(x)=8x^3
f'(x)=2(4)x^4-1
f(x)=2x^4
f(x)=15^2
f'(x)=5(3)x^3-1
Example : f(x)=5x^3
y'=f'(x)=nx^n-1
If y=f(x)=x^n

SYED MUHAMMAD ZUBAIR BIN SYED SHAHAZAM (052947) MSD 10503 DII

7. Quotient/ Rational Rule

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

5. Chain Rule

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

2. Constant-Multiple Rule

f'(x)=-3
f'(x)=5
f'(x)=dy/dx=m
if f(x)=mx
Where m is any constant

1. Constant Function/Rule

if f(x)=-7
f'(x)=0
Example : 1. if f(x)=4
dy/dx=f'(x)=0
if y = f(x)=c
where C is any constant