Calculus: Differentiation Techniques

 Assignment Questions

Section A – Short Answer Questions

1. If $y=\ln (\sin x)$, find $\frac{dy}{dx}$.

2. Differentiate $y=x^x$ with respect to $x$.

3. If $y={\tan }^{-1}\left(\frac{1+x}{1-x}\right)$, find $\frac{dy}{dx}$
   

4. If $x^2+y^2=25$, find $\frac{dy}{dx}$using implicit differentiation.

5. If $y=e^{\sin x}\cdot \cos x$, find $\frac{dydx}{}$
   

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Section B – Medium Answer Questions

6. If $y=\ln \left(\frac{1+x}{1-x}\right)$, find $\frac{dy}{dx}$ and simplify.

7. A function is given implicitly by $x^3+y^3=3xy$. Find $\frac{dy}{dx}$.

8. If $y={(x^2+1)}^{{\tan }^{-1}x}$, find $\frac{dy}{dx}$ using logarithmic differentiation.

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Section C – Long Answer Questions

9. 
   

   solution  
   
   

10.  x = e^(tan^(-1))((y-x^2)/x^2)  then find $\left(\frac{d\mathrm{y/}}{dx}\right)$ at $x=1$, x=2,x=3 

    
    
    
    

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