What is the derivative of y=tan^-1 sqrt(3x)?

2 Answers
Jun 7, 2016

dy/dx = 3/(2(1+3x)sqrt(3x))

Explanation:

Apply the chain rule in a straightforward manner.

dy/dx = 1/(1 + (sqrt(3x))^2) times 1/(2sqrt(3x)) times 3 = 3/(2(1+3x)sqrt(3x))

Jun 7, 2016

frac{d}{dx}(arctan (sqrt{3x}))=frac{sqrt{3}}{2sqrt{x}(3x+1)}

Explanation:

frac{d}{dx}(arctan (sqrt{3x}))

Applying chain rule,
frac{df(u)}{dx}=frac{df}{du}cdot frac{du}{dx}
Let ,sqrt(3x)=u
=frac{d}{du}(arctan (ut))frac{d}{dx}(sqrt{3x})
frac{d}{du}(arctan (u))=frac{1}{u^2+1}
frac{d}{dx}(sqrt{3x})=frac{sqrt{3}}{2sqrt{x}}
so,
=frac{1}{u^2+1}frac{sqrt{3}}{2sqrt{x}}
substitute back,u=\sqrt{3x}
=frac{1}{(sqrt{3x})^2+1}frac{sqrt{3}}{2sqrt{x}}

Simplifying back,
=frac{sqrt{3}}{2sqrt{x}(3x+1)}