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Differentiation Rules

1) Constant (d/dx) (c)=0

2) Power (d/dx) (xⁿ) = (n)x^(n-1)

 2a) (d/dx) x¹ = 1x⁰ = 1

3) Constant Multiplied (c)xn = (n)(c)(x(n-1))

4) Sum/Difference (d/dx) (f(x) ± g(x)) = (f '(x) ± g '(x))

5) Product Rule (d/dx) (f(x) * g(x)) = ((f(x)*g '(x)) + (f '(x)*g(x)))

Trig Functions:

Dx sin x = cos x

Dx cos x = sin x

Dx tan x = sec² x

Dx cot x = -csc² x

Dx sec x = sec x tan x

Dx csc x = -csc x cot x

Implicit Differentiation (Derivative when unable to separate all x's and y's on either side of the equation.)

Exp.

x*y = x

x*(dy/dx) + y = 1

dy/dx= (1-y)/x

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