Question Type 6: Learning to apply the quotient rule on all derivatives in fraction form Exercises

Differentiate $f(x) = \frac{3x^2 +5x -2}{2x^3 - x}$

Differentiate $f(x) = \frac{x^2 - 4}{x^3 + 1}$

Differentiate $f(x) = \frac{\sqrt{x} + \ln x}{x^2 +1}$ [4 marks]

Differentiate $f(x) = \frac{\sin(x)}{1+\cos(x)}$

Differentiate $f(x) = \frac{\arctan(x) + x^2}{x^3}$ [5 marks]

Differentiate $f(x) = \frac{x^3 -3x}{\sin(x)}$

Differentiate $f(x) = \frac{\sin(x) + \ln(x)}{3x^2}$

Differentiate $f(x) = \frac{xe^x}{x+2}$

Differentiate $f(x) = \frac{2x+1}{x^2}$ [3 marks]

Differentiate $f(x) = \frac{e^x + x}{x - 1}$

Differentiate $f(x) = \frac{\ln(x) + 1}{x^2 - x}$

Differentiate $f(x) = \frac{(x^2+1)e^x}{x}$