Question

Find f'(x) and simplify!

a) f(x)= sinx/(x^2)

b) f(x)= (3x^2 +2x -1)^4

c) f(x)= (x-5/2x+1)^2

Answer 1

`\bf f(x)=\cfrac{sin(x)}{x^2}\implies \cfrac{dy}{dx}=\cfrac{x^2cos(x)-2xsin(x)}{(x^2)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{x[xcos(x)-2sin(x)]}{x^4}\implies \cfrac{dy}{dx}=\cfrac{xcos(x)-2sin(x)}{x^3} \\\\ -----------------------------\\\\`


`\bf f(x)=(3x^2+2x-1)^4\implies \cfrac{dy}{dx}=4(3x^2+2x-1)^3(6x+2) \\\\ -----------------------------\\\\ f(x)=\left( \cfrac{x-5}{2x+1} \right)^2\implies \cfrac{dy}{dx}=2\left( \cfrac{x-5}{2x+1} \right)\left[ \cfrac{2x+1-2(x-5)}{(2x-1)^2} \right] \\\\\\ \cfrac{dy}{dx}=2\left( \cfrac{x-5}{2x+1} \right)\left[ \cfrac{11}{(2x-1)^2} \right]`