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Calculus(Properties)

Properties of Derivatives

FunctionPropertyDefinition
[f(x) + g(x)]' Power rule (addition) f'(x) + g'(x)
[f(x) - g(x)]' Power rule (subtraction) f'(x) - g'(x)
[f(x) * g(x)]' Product rule f'(x)g(x) +f(x)g'(x)
[f(x) / g(x)]' Quotient rule [f'(x)g(x) - f(x)g'(x)]/[g(x)]^2
[c f(x)]' Constant rule c f'(x)
ex) y=(x^2+1)^100 Chain Rule 200x(x^2+1)^99
ex) f(x)=x^5 * sinx properties 5x^4(sinx) + x^5(cosx) = x^4[(5sinx)+(xcosx)]
ex) f(x)=ln [sin(x^3)] chain 3x^2cotx^3
ex) sin (x^3+1) chain 3x^2 cos (x^3+1)
Created by: Alyssa