The following standard derivatives are stated in MF27 or follow directly from the standard trigonometric, exponential and logarithmic results. Inverse-trigonometric and reciprocal-trigonometric derivatives **Function** | **Derivative** | **Conditions** sin-1x | 1sqrt(1-x2) | |x|<1 cos-1x | - 1sqrt(1-x2) | |x|<1 tan-1x | 11+x2 | All real x cosec,x | -cosec,xcot x | Where defined sec x | sec xtan x | Where defined Trigonometric derivatives **Function** | **Derivative** sin x | cos x cos x | -sin x tan x | sec2x cot x | -cosec2x sec x | sec xtan x cosec,x | -cosec,xcot x Exponential and logarithmic derivatives **Function** | **Derivative** | **Conditions** ex | ex | All real x ax | axln a | a>0, a 1 ln x | 1x | x>0 log_a x | 1xln a | x>0, a>0, a 1

The following standard derivatives are stated in MF27 or follow directly from the standard trigonometric, exponential and logarithmic results.

Inverse-trigonometric and reciprocal-trigonometric derivatives