Question Type 5: Applying quotient rule on functions as a rational Exercises

Differentiate $\frac{x^2+1}{x-1}$ with respect to $x$.

Differentiate $\frac{\tan(x)}{x^2}$ with respect to $x$.

Differentiate $\frac{e^{-2x}}{x^2+3}$ with respect to $x$.

Differentiate $\frac{\sin(x)+\ln(x)}{3x^2}$ with respect to $x$.

Find the derivative of $\frac{[\ln(x)]^2}{x^3}$.

Differentiate $\frac{\ln(x)}{\sqrt{x}+1}$ with respect to $x$.

Find the derivative of $\frac{e^x+x^2}{\sin(x)}$.

Compute $\displaystyle \frac{d}{dx}\Bigl[\frac{x^3\cos(x)}{1+x^2}\Bigr]\,$.

Differentiate $\frac{\sin^2(x)}{\ln(x)}$ with respect to $x$.

Compute the derivative of $\frac{\sqrt{1+x^2}}{x\,e^x}$.

Find $\displaystyle \frac{d}{dx}\Bigl[\frac{\cos(\ln(x))\,e^{-x}}{x\ln(x)}\Bigr]\,$.

Find $\displaystyle \frac{d}{dx}\Bigl[\frac{x\,e^{x^2}}{\cos(x)}\Bigr]\,$.