Kalkulus (2) Turunan

$$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$$

$$\lim_{x\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$$

$$\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{x+h}$$

$$\lim_{x\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{x+h}$$

$$\frac{df\left(x\right)}{dx}$$  

$$\frac{dx}{dy}$$  

$$y'$$  

$$f'\left(x\right)$$  

$$f'\left(x\right)=u'v+uv'$$

$$f'\left(x\right)=u'-v'$$  

$$f'\left(x\right)=u'+v'$$  

$$f'\left(x\right)=\frac{u'v-uv'}{v^2}$$  

Kali, kurangi 1

Bagi, kurangi 1

Kali, tambah 1

Bagi, kurangi 1

$$y'=\frac{a}{n+1}x^{n+1}$$  

$$y'=\frac{a}{n}x^{n+1}$$  

$$y'=anx^{n-2}$$  

$$y'=anx^{n-1}$$  

$$2\ kali\ 5$$   $$x$$   $$^{5\ kurangi\ 1}$$  

$$2\ kali\ 5$$   $$x$$   $$^{5\ kurangi\ 2}$$  

$$5\ kali\ 2$$   $$x$$   $$^{2\ kurangi\ 1}$$   

$$5\ kali\ 2$$   $$x$$   $$^{5\ kurangi\ 5}$$  

$$y'=nu^{n-1}$$

$$y'=u'$$  

$$y'=nu^{n-1}.u'$$  

$$y'=nu$$  

$$y'=2$$

$$y'=12\left(2x-5\right)^3.2$$  

$$y'=12\left(2x-5\right)^3$$  

$$y'=12x^3$$  

$$f''\left(x\right)=\frac{2}{5}x^5-\frac{1}{4}x^4+2x^3-10x+C$$

$$f''\left(x\right)=2x^4-x^3+6x^2-10$$

$$f''\left(x\right)=8x^3-3x^2+12x$$

$$f''\left(x\right)=24x^2-6x+12$$

$$x<-3$$ atau $$x>1$$

$$-3<x<1$$

$$x<-1$$ atau $$x>3$$

$$-1<x<3$$

36 meter/detik

30 meter/detik

9 meter/detik

3 meter/detik