Basic Formulas of Limits and Derivatives in Class 11

Limits

1. $\lim\limits_{x \rightarrow a} c=c$

2. $\lim\limits_{x \rightarrow a} x=a$

3. $\lim\limits_{x \rightarrow a} x^n=a^n$

4. $\lim\limits_{x \rightarrow 0} \frac{\sin x}{x}=1$

5. $\lim\limits_{x \rightarrow 0} \frac{1-\cos x}{x}=0$

Derivatives

1. $\frac{d}{d x}(c)=0$

2. $\frac{d}{d x}\left(x^n\right)=n x^{n-1}$

3. $\frac{d}{d x}(\sin x)=\cos x$

4. $\frac{d}{d x}(\cos x)=-\sin x$

5. $\frac{d}{d x}\left(e^x\right)=e^x$