Basic Differential Rules
▼Refer to Math is fun: Derivative Rules
Rules | Function | Derivative |
Constant | c | 0 |
With constant | c·f | c·f’ |
Power Rule | xⁿ | n·xⁿ⁻¹ |
Sum Rule | f + g | f’ + g’ |
Difference Rule | f - g | f’ − g’ |
Product Rule | f · g | fg’ + f’ g |
Quotient Rule | f / g | (f’g − g’f ) / g² |
Reciprocal Rule | 1 / f | −f’ / f² |
Chain Rule | f(g(x)) | f’(g(x)) · g’(x) |
Exponent Rule | eˣ | eˣ |
aˣ | aˣ · ln(a) | |
Log Rule | ||
Natural Log Rule | ln(x) | 1/x |
Exponential Rule | ||
Trig Rules | sin(x) | cos(x) |
cos(x) | −sin(x) | |
tan(x) | sec²(x) = 1/cos²(x) | |
sec(x) | sec(x)·tan(x) | |
csc(x) | -csc(x)·cot(x) | |
cot(x) | −csc²(x) = -1/sin²(x) = -(1+cot²(x)) | |
Inverse Trig Rules | arcsin(x) | 1/√(1−x²) |
arccos(x) | −1/√(1−x²) | |
arctan(x) | 1/(1+x²) |
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