Mathematics · Ch 8 — Differentiation
Table 1.2.1 — Derivatives of Standard Inverse Trigonometric Functions
Table 1.2.1 — Derivatives of Standard Inverse Trigonometric Functions
The six derivatives proved (or set as homework) in the previous section are gathered here into one reference table, each paired with the exact -domain and -range (principal branch) that the formula depends on — since an inverse trig function is only single-valued, and hence only differentiable in the ordinary sense, once its branch …
y = sin^-1 x : dy/dx = 1/sqrt(1-x^2), |x|<1 ; conditions -1<=x<=1, -pi/2<=y<=pi/2
y = cos^-1 x : dy/dx = -1/sqrt(1-x^2), |x|<1 ; conditions -1<=x<=1, 0<=y<=pi
y = tan^-1 x : dy/dx = 1/(1+x^2) ; conditions x in R, -pi/2<y<pi/2
y = cot^-1 x : dy/dx = -1/(1+x^2) ; conditions x in R, 0<y<pi
y = sec^-1 x : dy/dx = 1/(x sqrt(x^2-1)) for x>1, = -1/(x sqrt(x^2-1)) for x<-1 ; conditions |x|>=1, 0<=y<=pi, y != pi/2 …