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Derivative Rules

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  • f(x)=(h(x))/(g(x)),then f'(x)=(g'⋅h(x)-g(x)⋅h'(x))/〖[h(x)]〗^2
    Quotient Rule
  • 𝑓 ( 𝑥 ) = 𝑔 ( 𝑥 ) − ℎ ( 𝑥 ) f(x)=g(x)−h(x), then 𝑓′( 𝑥 ) = 𝑔′( 𝑥 ) − ℎ′( 𝑥 ) f′(x)=g′(x)−h′(x)
    Difference Rule
  • f(x)=g(x)+h(x), then 𝑓′( 𝑥 ) = 𝑔′( 𝑥 ) + ℎ′ ( 𝑥 ) f ′ (x)=g ′ (x)+h ′ (x).
    Sum Rule
  • f(x)=c (where 𝑐 c is a constant), then 𝑓′( 𝑥 ) = 0 f′(x)=0.
    Constant Rule
  • f(x)=g(h(x)), then 𝑓 ′ (𝑥) = 𝑔 ′( ℎ ( 𝑥 ) ) ⋅ ℎ ′( 𝑥 )f ′(x)=g′(h(x))⋅h′(x)
    Chain Rule
  • f(x)=x^n then f′(x)=n⋅x^ n−1
    Power Rule
  • 𝑓 (𝑥) = 𝑔 (𝑥) ⋅ ℎ (𝑥) f(x)=g(x)⋅h(x), then 𝑓′ (𝑥) = 𝑔′ (𝑥) ⋅ ℎ (𝑥) + 𝑔 (𝑥) ⋅ ℎ′(𝑥) f′(x)=g′(x)⋅h(x)+g(x)⋅h′(x).
    Product Rule
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