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Derivatives of standard functions formulas
12 formulas for Derivatives of standard functions, from the Calculus section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Constant | d/dx (c) = 0 | |
| Power | d/dx (xⁿ) = n·xⁿ⁻¹ | |
| Exponential | d/dx (eˣ) = eˣ; d/dx (aˣ) = aˣ ln a | |
| Logarithm | d/dx (ln x) = 1/x; d/dx (logₐ x) = 1/(x ln a) | |
| sin, cos | d/dx sin x = cos x; d/dx cos x = −sin x | |
| tan, cot | d/dx tan x = sec²x; d/dx cot x = −cosec²x | |
| sec, cosec | d/dx sec x = sec x tan x; d/dx cosec x = −cosec x cot x | |
| sin⁻¹, cos⁻¹ | ± 1/√(1 − x²) | |
| tan⁻¹, cot⁻¹ | ± 1/(1 + x²) | |
| sec⁻¹ | 1/(|x|√(x² − 1)) | |
| √x | 1 / (2√x) | |
| 1/x | −1/x² |
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