Question

write all formulas of derivative

Answer 1

General Derivative Formulas:

1) ddx(c)=0 where c is any constant.

2) ddxxn=nxn−1 is called the Power Rule of Derivatives.
ddxx=1ddxx=1

4) ddx[f(x)]n=n[f(x)]n−1ddxf(x)ddx[f(x)]n=n[f(x)]n−1ddxf(x) is the Power Rule for Functions.

5) ddxx−−√=12x√ddxx=12x

6) ddxf(x)−−−−√=12f(x)√ddxf(x)=12f(x)√f′(x)ddxf(x)=12f(x)ddxf(x)=12f(x)f′(x)

7) ddxc⋅f(x)=cddxf(x)=c⋅f′(x)ddxc⋅f(x)=cddxf(x)=c⋅f′(x)

8) ddx[f(x)±g(x)]=ddxf(x)±ddxg(x)=f′(x)±g′(x)ddx[f(x)±g(x)]=ddxf(x)±ddxg(x)=f′(x)±g′(x)

9) ddx[f(x)⋅g(x)]=f(x)ddxg(x)+g(x)ddxf(x)ddx[f(x)⋅g(x)]=f(x)ddxg(x)+g(x)ddxf(x) is called the Product Rule.

10) ddx[f(x)g(x)]=g(x)ddxf(x)−f(x)ddxg(x)[g(x)]2ddx[f(x)g(x)]=g(x)ddxf(x)−f(x)ddxg(x)[g(x)]2 is called the Quotient Rule.

 

Derivative of Logarithm Functions: 

11) ddxlnx=1xddxln⁡x=1x

12) ddxlogax=1xlnaddxlogax=1xln⁡a

13) ddxlnf(x)=1f(x)ddxf(x)