Derivatives of Inverse Trig

$\frac{d}{dx}\left(\sin^{-1}x\right)=$

• $\frac{1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{-1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{1}{\sqrt{1+x^2}}$

• $\frac{-1}{\sqrt{1-x^2}}$

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.TF.B.7

 $\frac{d}{dx}\left(\sin^{-1}x\right)=$ 

• $\frac{1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{-1}{\sqrt{1-x^2}},\ x\ne\pm1$

•  $\frac{1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$ 

•  $\frac{-1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$ 

 $\frac{d}{dx}\left(\cos^{-1}x\right)=$ 

• $\frac{1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{-1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{1}{\sqrt{1+x^2}}$

• $\frac{-1}{\sqrt{1-x^2}}$

$\frac{d}{dx}\left(\cos^{-1}x\right)=$

• $\frac{1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{-1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$

• $\frac{-1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$

 $\frac{d}{dx}\left(\tan^{-1}x\right)=$ 

• $\frac{1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{-1}{\sqrt{1-x^2}},\ x\ne\pm1$

•  $\frac{1}{1+x^2}$ 

•  $\frac{-1}{1+x^2}$ 

Tags

CCSS.HSF.TF.B.7

$\frac{d}{dx}\left(\tan^{-1}x\right)=$

• $\frac{1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$

• $\frac{-1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$

• $\frac{1}{1+x^2}$

• $\frac{-1}{1+x^2}$

 $\frac{d}{dx}\left(\cot^{-1}x\right)=$ 

• $\frac{1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{-1}{\sqrt{1-x^2}},\ x\ne\pm1$

•  $\frac{1}{1+x^2}$ 

•  $\frac{-1}{1+x^2}$ 

Tags

CCSS.HSF.TF.B.7

 $\frac{d}{dx}\left(\cot^{-1}x\right)=$ 

•  $\frac{1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$ 

•  $\frac{-1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$ 

• $\frac{1}{1+x^2}$

• $\frac{-1}{1+x^2}$

 $\frac{d}{dx}\left(\sec^{-1}x\right)=$ 

•  $\frac{1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$ 

•  $\frac{-1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$ 

• $\frac{1}{1+x^2}$

• $\frac{-1}{1+x^2}$

 $\frac{d}{dx}\left(\sec^{-1}x\right)=$ 

• $\frac{1}{\sqrt{1-x^2}},\ x\ne\pm1$

• $\frac{-1}{\sqrt{1-x^2}},\ x\ne\pm1$

•  $\frac{1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$ 

•  $\frac{-1}{x\sqrt{x^2-1}},\ x\ne\pm1,0$