Differentiation

The Derivative and its basic rules

Power Rule

Chain Rule

Product Rule

Quotient Rule

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d/dx (ax^n) = anx^(n-1)

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dy/dx = u(ddx(v)) + v(ddx(u)) :

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d/dx tanf(x) = f'(x)sec^2x

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d/dx cosf(x) = -f'(x)sinx

the derivative is also known as dy/dx or the gradient function

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if y = ax^n, then dy/dx = ax^(n-1)

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Use quotient rule when:

  1. Both numerator and denominator contain variable x
  2. Denominator is a linear expression

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Use product rule:
1.there is only one term at denominator --> split the fraction into a few terms and differentiate term by term
2.During splitting, express each term in index form

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