(U∙V)'=U' V+UV'

(U∙V)'=U' V-UV'

(U∙V)'=U' ∙ V'

$$\left(\frac{U}{V}\right)'=\frac{U'V-UV'}{V^2}$$

$$\left(\frac{U}{V}\right)'=\frac{U'}{V'}$$

$$\left(\frac{U}{V}\right)'=\frac{UV'-UV'}{V^2}$$

$$tg\ \alpha\ =f'\left(x_0\right)$$  

$$tg\ \alpha\ =f\left(x\right)$$  

$$tg\ \alpha\ =f'\left(x\right)$$  

$$y=f\left(x_0\right)+f'\left(x_0\right)\cdot\left(x-x_0\right)$$  

$$y=f\left(x\right)+f'\left(x\right)\cdot\left(x-x_0\right)$$  

$$y=f'\left(x\right)+f'\left(x_0\right)\cdot\left(x-x_0\right)$$  

$$V\left(t\right)=S'\left(t\right)$$  

$$V\left(t\right)=S\left(t\right)$$  

$$S\left(t\right)=V'\left(t\right)$$  

$$C'=0$$  

$$C'=1$$  

$$C'=-1$$  

$$y'=\frac{1}{2\ \sqrt[]{x}}$$  

$$y'=\frac{1}{\sqrt[]{x}}$$  

$$y'=2\ \sqrt[]{x}$$  

$$y'=k$$  

$$y'=b$$  

$$y'=k+b$$  

$$y'=n\cdot x^{n-1}$$  

$$y'=n\cdot x^n$$  

$$y'=x^{n-1}$$  

2x+12x³

2x-12x³

2+12x

 $\cos x-\sqrt{x}$ 

 $-\sin x+\frac{1}{2\sqrt{x}}$ 

 $-\sin x-\frac{1}{2\sqrt{x}}$  

3cos3x

cos3x

3xsin3x

3sinx

$$y'=x'\cdot\cos x+x\cdot\left(\cos x\right)'$$

$$y'=\sin x+x\cdot\cos x$$

$$y'=x\cdot\sin x-x\cdot\cos x$$

$$y'=\cos x+x\cdot\sin x$$

v=1 (м/с)

v=2 (м/с)

v=3 (м/с)

v=4 (м/с)

0

4

$$\ln5-1$$  

$$5\left(\ln5-1\right)$$  

 $у^,=15\left(2х-5\right)^{14}$  

 $у^,=30\left(2х-5\right)^{14}$  

 $у^{,\ }=\left(2х-5\right)^{14}$  

 $у^,=-30\left(2х-5\right)^{14}$  

cos²x

-sin²x

2cosxsinx

-2cosxsinx

 $1+3^x\ln3$  

 $3^x\left(1+x\right)$  

 $3^x\left(1+x\ln3\right)$  

 $1+3^x$  

 $e^x\cdot\frac{1}{\sin^2x}$  

 $e^x\left(tg\ x+\ \frac{1}{\cos^2x}\right)$  

 $e^x\cdot\frac{1}{\cos^2x}$  

 $e^x\left(tg\ x+\frac{1}{\sin^2x}\right)$  

0

$$-\pi$$

-1

$$\pi$$

 $e^{\sin x}$  

 $e^{\sin x}\cos x$  

 $-e^{\sin x}\cos x$  

 $e^{\sin x}\sin x$