Calculus Solutions Ex#2.4

  Q.01-04 Compute the derivative of  $f(x)$ by (a) multiplying and then differentiating and (b) using the product rule. The product rule $$ \frac{d}{d x}[f(x) g(x)]=f(x) \frac{d}{d x}[g(x)]+g(x) \frac{d}{d x}[f(x)] $$ The quotient rule $$ \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]=\frac{g(x) \frac{d}{d x}[f(x)]-f(x) \frac{d}{d x}(g(x)]}{[g(x)]^2} $$ Solution: 1.(a )$$ f(x)=(x+1)(2 x-1) $$ $$ f(x)=2 x^2-x+2 x-1=2 x^2+x-1 $$ differentiating … Read more