Find the derivatives of the following: (i) y = -2/(x+1)^2 - x^2/(3x-1)

Question

Find the derivatives of the following:

(i) y = \(\frac{-2}{(x+1)^2} - \frac{x^2}{3x - 1}\)

(ii) y = \(\frac{sinx}{x}\)

(iii) y = \( \frac{ax + b}{cx + d}\)

(iv) y = \(\frac{1+tanx}{1-tanx}\)

Answer 1

(i)

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

(ii) 

(iii) 

= \(\frac{(cx + d)a - (ax + b)c}{(cx + d)^2}\)

= \(\frac{acx + ad - acx - bc}{(cx + d)^2}\)

= \(\frac{ad - bc}{(cx + d)^2}\)

(iv)