Find the derivatives of the following :

Q1. f(x) = \(\frac{x^2+3x+7}{x^2+3x-4}\)

Ans:  The derivative is f'(x) =- \(\frac{11(2x+3)){(x^2+ 3x-4)}\)

Q2. g(x) = \(\sqrt{x^-4x}\)

Ans: The derivative is g'(x) = \(\frac{x-2}{\sqrt{x^2-4x}}\)

Q3.h(x) = In(\(\frac{x-1}{x+4}\))

Ans: \(\frac{5}{(x-1)(x+4)}\)

Q4. u(x) = \(\frac{x^2-1}{x^3+1}\)

Ans : The derivative is u'(x) = –\(\frac{x(x-2)}{(x^2-x+1)^2}\)

Q5.v(x)  = \(e^{x^2+2x+1}\)

Ans:  The derivative is v'(x) = \((2x+2)e^{x^2+2x+1}\)