Question

hi, how many principles of differentiation is there? can anyone please state them (with formulas) for me?

Answer 1

I can help what subject is this?

Answer 2

calculus

Answer 3

okay first tell me what you know

Answer 4

nvm there are 5 principles

Answer 5

wow...ok

Answer 6

i know differentiation and integration in first principle

Answer 7

i never knew of the other principles

Answer 8

i know how to find the various derivatives and integrals...thats all.

Answer 9

I didn't either lol but its quite simple www.pkwy.k12.mo.us/candd/.../gifted/PrinciplesofDifferentiation.htm this can help you

Answer 10

okay...I'd try it out and get back to you

Answer 11

Thanks for the help

Answer 12

\[.\newcommand \de [2] {\displaystyle\frac{\mathrm d #1}{\mathrm d#2}} % first order derivative\]
CONSTANT RULE
The derivative of a constant equals zero.
\[\boxed{\de{}x(c)=0\qquad c\in \mathbb R}\]\[c' = 0\]

POWER RULE
The derivative of a power of \(x\),
equals the power multiplied by \(x\) to the power reduced by one.
\[\boxed{\de{}x(x^n) = nx^{n-1}}\]

SUM RULE
The derivative of a sum, equals the sum of the derivatives.
\[\boxed{\de{}x(f + g) = \de fx + \de gx}\]\[(f + g)' = f' + g'\]

PRODUCT RULE
The derivative of a product equals,
the the derivative of the first term multiplied by the second term,
plus the first term multiplied by the derivative of the second term.
\[\boxed{\de {}x(f\cdot g) = \de fx\cdot g + f\cdot\de gx}\]\[(f\cdot g)' = f'\cdot g + f\cdot g'\]

QUOTIENT RULE
The derivative of a quotient,
equals the derivative of the numerator multiplied by denominator,
minus the numerator multiplied by the derivative of the denominator,
all divided by the square of the denominator.
\[\boxed{\de{}x\Big(\frac fg\Big) = \frac{\de fx\cdot g-f\cdot\de gx}{g^2}}\]

CHAIN RULE
The derivative of a composition,
equals the composition of the derivative of the first term with the second term,
multiplied by the derivative of the second term.
\[\boxed{\de {}x(f\circ g) = \de fg\cdot\de gx}\]\[\big(f\circ g\big)' = (f'\circ g)\cdot g'\]