Calculus

There are 2 kinds of calculus :

1.deferential calculus/differentiation 2.integral calculus/integration

⇕ ৷ ⇕

অন্তরীকরণ /ব্যবকলন যোগজীকরণ/সমাকলন

Differential operators

Δ/δ = the rate of changing

dx d= differential operator

→ = tends to

Slope

Positive slope,negative slope,zero slope,undefined slope

The formula of determining slope : tanθ=ΔxΔy

Differential laws

1.dxd(xn)=nxn−1

2.dxd(cxn)=c×dxd(xn)

3.dxd(c)=04.dxd(x+y+...)=dxd(x)+dxd(y)+...5.dxd(xy)=xdxd(y)+ydxd(x)6.dxd(lnx)=x17.dxd(sinx)=cosx8.dxd(cosx)=−sinx

9.dxd(tanx)=sec2x10.dxd(cotx)=−csc2x11.dxd(secx)=secxtanx

1.dxd(cscθ)=−cscxcotx

The relation between differentiation and integration

If we differentiate a function we get the function back by integration. More simply, "a function's" differential value is "x" then, its integral value will be "that function".