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BC Calc - Unit 3
| Question | Answer |
|---|---|
| Derivative Of "ln(a^n)" | (n)(lna) |
| Derivative Of "a^x" | (lna)(a^x) |
| Derivative Of "logax" | (1/lna) ⋅ lnx |
| Derivative Of "a^u" | (lna)(a^u)(u') |
| Derivative Of "logau" | (1/(lna ⋅ u)) (u') |
| Decomposing Composite Functions | rewrite function using parenthesis, set "g(x)"/inside function equal to "u", rewrite as y set equal to f(u) |
| "u" Is The... | inside function |
| Implicit Differentiation | 1) differentiate both sides in respect to x ;; 2) separate x and y terms ;; 3) factor out y' ;; 4) solve for y' |
| The Slope Is Equal To... | the derivative of the function |
| Derivative Of "x^e" | e ⋅ x^(e-1) |
| "(inverse f)'(x)" Is Equal To... | 1/(f'(inverse f(x))) |
| Derivative Of "arcsinu" | u'/√(1-u^2) |
| Derivative Of "arccosu" | -u'/√(1-u^2) |
| Derivative Of "arctanu" | u'/(1+u^2) |
| Derivative Of "arccotu" | -u'/(1+u^2) |
| Derivative Of "arcsecu" | u'/|u|√(u^2-1) |
| Derivative Of "arccscu" | -u'/|x|√(u^2-1) |
| When Deriving "arc-trigfunction(x)", The Numerator Of The Derivative Is... | ±1 (depends on function) |
| Position, Velocity, & Acceleration Relationship By Derivatives | p' = v // v'=a // p''=a |
| Position, Velocity, & Acceleration Relationship By Intergrals | ∫a = v // ∫v=p |
Created by:
abievans
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