$\left(-x^2\right)^I\ =\ -2x^2$

$\left(2x^3\right)^I\ =\ 6x^2$

$\left(\ 4x\ -2x^3\right)^I\ =\ 4\ -\ 6.x^2$

$\left(-\sin x\right)^I\ =\ -\cos x$

$\left(\cos x\right)^I\ =\ -\sin x$

$\left(\cos x-\sin x\right)^I\ =\ -\cos x-\sin x$

$\left(\ u\ +v\right)^I\ =\ u^I\ +\ v^I$

$\left(u\ -\ v\right)^I\ =\ u^I\ -\ v^I$

$\left(\ u.v\right)^I\ =\ u^I.v\ -\ v^I.u$

$\left(\frac{u}{v}\right)^I\ =\ \frac{u^I.v\ +\ v^I.u}{v^2}$

6x - 6

6x² - 6x

6x² - 6

6x³ - 6x²

4x³ - 4x² - 4

4x³ - 12x² - 4

4x² - 12x - 4

4x³ - 12x² - 4x

 $\frac{1}{2x}$  

 $-x^{-1}$  

 $\frac{1}{x^2}$  

-x^-2

f ''(x)= 2 - 20x

f ''(x) = 2 - 20x⁴

f ''(x) = 2x - 20x³

f ''(x) = 2 - 20x

2.sin 2x

-2.sin 2x

-sin 2x

sin 2x

 $\frac{2}{\left(x+1\right)^2}$  

 $\frac{-2}{\left(x+1\right)^2}$  

 $\frac{2x}{\left(x+1\right)^2}$  

 $\frac{-2x}{\left(x+1\right)^2}$  

3

6

9

12

1

-1

 $\frac{1}{2}$  

 $-\frac{1}{2}$  

 $3.\sin^2x$  

 $3.\sin^2x.\cos x$  

 $3.\cos^2x.\sin x$  

 $-3.\sin^2x.\cos x$  

8

-8

4

-4

 $\frac{\cos x-x.\sin x}{\cos^2x}$  

 $\frac{\cos x+x.\sin x}{\cos^2x}$  

 $\frac{x.\cos x+\sin x}{\cos^2x}$  

 $\frac{x.\sin x-\cos x}{\cos^2x}$  

5

4

3

-4

 $2x.\cos x-x^2.\sin x$  

 $2x.\cos x+x^2.\sin x$  

 $2x.\sin x-x^2.\cos x$  

 $2.\cos x-x^2.\sin x$  

 $6.\left(3-2x\right)^2$  

 $-6.\left(\ 3\ -2x\right)^3$  

 $-6.\left(3\ -2x\right)^2$  

 $-6.\left(3\ -\ 2x\right)^3$  

1

2

3

4