Limits
lim as x approaches -3 of (3x+2)
-7
f(x)=x^3/5 +2
f'(x)=3/(5*5th root of (x^2))
integral from 0 to 3 of (2x-1) dx
6
Def of a derivative function
f'(x)=lim as h approaches 0 of f(x+h)-f(x) / h
integral of 2x / (x^2+5)^4 (dx)
-1/3(x^2+5)^3 +C
lim as x approaches -1 of (x^3-1)/(x-1)
1
f(x)=x^4/7
f'(x)=4/(7*7th root of (x^3))
integral from 1 to 3 of 2x+3dx
14
Derivative Formula 1
d/dx k =0
integral of 15x^6 times sqrt3x^5+5 dx
2(3x^5+5) sqrt 3x^5+5 /3 +C
lim as x approaches -1 of (2x^2-x-3)/x+1
-5
f(x)=|2x+1|
f'(x)=(4x+2)/|2x+1|
integral from 1 to 2 of (1/x)dx
ln(2)
Derivative Formula 2
d/dx (k*f(x))=k*f'(x)
sort of (x^3-2)^=4 *3x^2 dx
-1/3(x^3-2)^3 +C
lim as x approaches 0 to the negative side of (x+1)/x
-infinity
f(x)=3x^2/3 /x^3+1
f'(x)=-7x^3+2 / 3rd root of x *(x^3+1)^2
integral from 1 to e of 1/x dx
1
d/dx e^f(x)=e^f(x) *f'(x)
integral of 15x^2 sort 5x^3-2 dx
2(5x^3-2) sqrt 5x^3-2 / 3 +C
lim as x approaches 3 to the positive side of x/(x^2-2x-3)
positive infinity
f(x)=4x^3/4 *(3x^4-1)
f'(x)=(57*|x|*|x^3|-3)/4th root of x
integral from 0 to pi of sina da
2
Tangent and normals
y-f(a)=f'(a)(x-a)
integral of 6x/(3x^2+2)^3 dx
-1/2(3x^2+2)^2 + C