Question

What is the derivative of `cosh^(-1)(sqrt(4x)+1)`?

Answer 1

`d/(dx)cosh^(-1)(sqrt(4x)+1)=1/(2sqrt(x^2+xsqrtx))`

Explanation:

As derivative of `cosh^(-1)x=1/sqrt(x^2-1)`

`d/(dx)cosh^(-1)(sqrt(4x)+1)`

= `1/sqrt((sqrt(4x)+1)^2-1)xx4/(2sqrt(4x))`

= `1/sqrt(4x+1+2sqrt(4x)-1)xx1/sqrtx`

= `1/(2sqrt(x+sqrtx))xx1/sqrtx`

= `1/(2sqrt(x^2+xsqrtx))`