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Common Derivatives
Common derivatives found in AB Calculus
| Term | Definition |
|---|---|
| Derivative Definition | (f(x+h)-f(x))/h |
| Cont Checklist #1 | f(a) is defined |
| Cont Checklist #2 | lim(x-->a) f(x) exists |
| Cont Checklist #3 | lim(x-->a) f(x) = f(a) |
| Constant Rule | f(x) = c; f'(x) = 0 |
| Power Rule | f(x) = x^n; f'(x) = nx^n-1 |
| Sum Rule | f(x) = u+v; f'(x) = u'+v' |
| Product Rule | f(x)=u*v; f'(x)=u*v' + v*u' |
| Quotient Rule | f(x)=u/v; f'(x)=(vu'+uv')/v^2 |
| Sine | cos(x) |
| Cosine | -sin(x) |
| Tangent | sec^2(x) |
| Cotangent | -csc^2(x) |
| Secant | sec(x)tan(x) |
| Cosecant | -csc(x)cot(x) |
| Logarithmic | f(x)=logb(x); f'(x)=1/(x*ln(b)) |
| Natural Log | 1/x |
| Exponential | b^x*ln(b) |
| Natural Exponential | e^x |
| Inverse | 1/f'(x0), y0=f(x0) |
| Sine Inverse | 1/(sqrt(1-x^2)) |
| Cosine Inverse | -1/(sqrt(1-x^2)) |
| Tangent Inverse | 1/(1+x^2) |
| Cotangent Inverse | -1/(1+x^2) |
| Secant Inverse | 1/(|x|sqrt(x^2-1)) |
| Cosecant Inverse | -1/(|x|sqrt(x^2-1)) |
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