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Calculus 1: formulas

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The formulas are for Calculus 1: course.

1. $f^{\prime}(a)=\lim\limits_{h\rightarrow0}\dfrac{f(a+h)-f(a)}{h}$

2. $(x^{k})^{\prime}=kx^{k-1}$

3. $(e^{x})^{\prime}=e^{x}$

4. $(\ln x)^{\prime}=\dfrac{1}{x}$

5. $(\sin x)^{\prime}=\cos x$

6. $(\cos x)^{\prime}=-\sin x$

7. $(\tan x)^{\prime}=\sec^{2}x$

8. $(\arcsin x)^{\prime}=\dfrac{1}{\sqrt{1-x^{2}}}$

9. $(\arccos x)^{\prime}=-\dfrac{1}{\sqrt{1-x^{2}}}$

10. $(\arctan x)^{\prime}=\dfrac{1}{1+x^{2}}$

11. $(f+g)^{\prime}=f^{\prime}+g^{\prime}$

12. $(kf)^{\prime}=kf^{\prime}$

13. $(uv)^{\prime}=u^{\prime}v+v^{\prime}u$

14. $(\dfrac{u}{v})^{\prime}=\dfrac{u^{\prime}v-v^{\prime}u}{v^{2}}$

15. $(f\circ g)^{\prime}(a)=f^{\prime}(g(a))\cdot g^{\prime}(a)$

16. $(f^{-1}(a))^{\prime}=\dfrac{1}{f^{\prime}(f^{-1}(a))}$