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Calculus Derivatives
Rules of derivatives for differential calculus. Source: Math is Fun.
| Function/Rule Name | Function/Rule | Derivative |
|---|---|---|
| Constant Function | f(x) = b | 0 |
| Line Function | f(x) = x | 1 |
| Quadratic Function | f(x) = x^2 | 2x |
| Cubic Function | f(x) = x^3 | 3x^2 |
| Square Root Function | f(x) = x^(1/2) | 1/2(x^(-1/2)) |
| Cube Root Function | f(x) = x^(1/3) | 1/3(x^(-2/3)) |
| Exponential Function | f(x) = a^x | ln(a) a^x |
| Logarithmic Function | f(x) = log_a(x) | 1/(ln(a) x) |
| Sine Function | f(x) = sin(x) | cos(x) |
| Cosine Function | f(x) = cos(x) | -sin(x) |
| Tangent Function | f(x) = tan(x) | (sec(x))^2 |
| Inverse Sine Function | f(x) = arcsin(x) | 1/((1-x^2)^(1/2)) |
| Inverse Cosine Function | f(x) = arccos(x) | -1/((1-x^2)^(1/2)) |
| Inverse Tangent Function | f(x) = arctan(x) | 1/(1+x^2) |
| Derivative | d/dx | ’ |
| Multiplication by Constant | cf(x) | cf’(x) |
| Power Rule | x^n | nx^(n-1) |
| Sum Rule | f(x)+g(x) | f’(x)+g’(x) |
| Difference Rule | 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)*f(x))/(g(x)^2) |
| Reciprocal Rule | 1/f(x) | -f(x)/(f(x)^2) |
| Chain Rule | f(g(x)) | f’(g(x))*g’(x) |
| General Derivative Formula | d/dx f(x) | (f(x+h)-f(x))/h |
Created by:
Nitrogen7
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