Derivative and Quotient Rule Problems

If $$y = \frac{f(x)}{g(x)}$$ , then the derivative is given by $$y' = \frac{g(x)f' - f(x)g'}{(g(x))^2}$$ .

$$f'(x) = 21x^6 - 36x^5 - 40x^3 + 9x^2 - 15$$ .

$$y' = \frac{3x^2 - 2x}{(3x - 1)^2}$$ .

$$g'(x) = \frac{3(x^2 + 2) - (3x - 2)(2x)}{(x^2 + 2)^2} = \frac{3x^2 + 4x + 6}{(x^2 + 2)^2}$$ .

Use the Quotient Rule: If $$y = \frac{f(x)}{g(x)}$$ , then $$y' = \frac{g(x)f' - f(x)g'}{(g(x))^2}$$ .

$$h'(1) = 18$$ .

$$y' = \frac{g(x)f' - f(x)g'}{(g(x))^2}$$ .

$$f'(x) = 3x^2 + 4x - 5$$ .

$$f'(x) = \frac{(x - 1)(2x) - (x^2 + 1)(1)}{(x - 1)^2}$$ .

$$f'(x) = \frac{(2x^2 + 3)(15x^2) - (5x^3)(4x)}{(2x^2 + 3)^2}$$ .