Похідна функції. 02,04

$u^{\prime}\left(x\right)+v^{\prime}\left(x\right)$

$u^{\prime}\left(x\right)-v^{\prime}\left(x\right)$

$Cu^{\prime}\left(x\right)$

$\left(u\left(x\right)\cdot v\left(x\right)\right)^{\prime}$

$u^{\prime}\left(x\right)+v^{\prime}\left(x\right)$

$u^{\prime}\left(x\right)-v^{\prime}\left(x\right)$

$\left(Cu\left(x\right)\right)^{\prime}=Cu^{\prime}\left(x\right)$

$\left(u\left(x\right)\cdot v\left(x\right)\right)^{\prime}$

$u^{\prime}\left(x\right)+v^{\prime}\left(x\right)$

$u^{\prime}\left(x\right)-v^{\prime}\left(x\right)$

$Cu^{\prime}\left(x\right)$

$u^{\prime}\left(x\right)\cdot v\left(x\right)+u\left(x\right)v^{\prime}\left(x\right)$

$\left(u\left(x\right)+v\left(x\right)\right)^{\prime}^{}=u^{\prime}\left(x\right)+v^{\prime}\left(x\right)$

$\left(u\left(x\right)-v\left(x\right)\right)^{\prime}=u^{\prime}\left(x\right)-v^{\prime}\left(x\right)$

$\left(Cu\left(x\right)\right)^{\prime}=Cu^{\prime}\left(x\right)$

$\left(u\left(x\right)\cdot v\left(x\right)\right)^{\prime}=u^{\prime}\left(x\right)\cdot v\left(x\right)+u\left(x\right)v^{\prime}^{}\left(x\right)$

0

1

2

y

0

1

-1

y

0

2x

x²

2x²

0

2x

x⁴

4x³

0

6x

3x²

3x³

$f^{\prime}\left(x\right)>0$

$f^{\prime}\left(x\right)<0$

$f^{\prime}\left(x\right)>0$

$f^{\prime}\left(x\right)<0$

0

2x²+3x

2x+3

2x³+3x²+5x

0

3x²+6x+3

2x+3

3x²+8x+3

4x³-6x²+6x-6

4x³-5x²+5x-6

4x⁴-5x⁵+6x-7

x²-15

5x⁴-6x³-3x²+2x-4

10x⁴-8x³-9x²+4x-4

8x³-6x²+6x-4

20x⁴-8x³+6x-4

6x⁵+5x⁴+4x³+3x²+2x+1

x⁵+x⁴+x³+x²+x+1

5x⁵+4x⁴+3x³+2x²+x+1

6x⁵+3x²

6x⁵-5x⁴-4x³-3x²-2x-1

x⁵-x⁴-x³-x²-x-1

5x⁵-4x⁴-3x³-2x²-x-1

6x⁵-3x²

-2

2

0

-$\sqrt4$

-0,25

2,5

0

-$\frac14$

$\sqrt{x}$

$\frac{1}{2\sqrt{x}}$

0

$\sqrt{2x}$

$\sqrt{x}$

$\sin x$

$-\sin x$

$\cos x$