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Calculus(Properties)
Properties of Derivatives
Function | Property | Definition |
---|---|---|
[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) |