Find the derivative of arccos((x+1)/3)

 Exercise

$\frac{d}{dx}\left(arc\cos\frac{x+1}{3}\right)$

 

Taking the derivative of arccosine

$\frac{-1}{\sqrt{1-\left(\frac{x+1}{3}\right)^2}}\frac{d}{dx}\left(\frac{x+1}{3}\right)$

 

The derivative of a function multiplied by a constant ($\frac{1}{3}$) is equal to the constant times the derivative of the function

$\frac{1}{3}\frac{-1}{\sqrt{1-\left(\frac{x+1}{3}\right)^2}}\frac{d}{dx}\left(x+1\right)$

 

Multiplying fractions $\frac{-1}{\sqrt{1-\left(\frac{x+1}{3}\right)^2}} \times \frac{1}{3}$

$\frac{-1}{3\sqrt{1-\left(\frac{x+1}{3}\right)^2}}\frac{d}{dx}\left(x+1\right)$

 

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{-1}{3\sqrt{1-\left(\frac{x+1}{3}\right)^2}}$

$\frac{-1}{3\sqrt{1-\left(\frac{x+1}{3}\right)^2}}$

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