Integrals
int (-20x^9) \ dx
-2x^10 + c
y= 3x3-10x2+6x-5
y'=9x^2-20x+6
int_0^4(2x)\dx
16
The slope of the tangent line at any point of the curve
Derivative
int \ dx
x + c
int (e) \ dx
ex + c
y= ln (3x3+4x2-2x)
y'= (9x^2+8x+2)/(3x^3+4x^2-2x)
int_-4^4 (3/5x+4) \ dx
32
To find the intervals where the function is increasing or decreasing you use...
The first derivative
int ((7x^5-5x^4-2x)/x^3) \ dx
(7x^3)/3-(5x^2)/2+2/x+c
int (3/(x^3)) \ dx
-3/(2x^2) + c
y= (2x^2+6)(4x-2)
y'=24x^2-8x+24
int_-2^1(-11/7x+3) \ d(x)
159/14 or 11.36
Is used in calculus to determine the local Maximum and/or the local Minimum Points.
Second Derivative
FIND y' of y=(2x+1)^2
y'= 8x+4
int (1/sqrt(x)) \ dx
2sqrt(x) + c
y= sin(3x)+ cos(x^2)
y'= 3cos(3x)-2x sin(x^2)
int_0^2 (3m^2-5m-2) \ dm
-6
The way of inverse process of differentiation.
Integrals
Which is my full name
Ana Rocío Espino Zubieta y Landa
int (5 \root(3)(x)) \ dx
(15root(3)(x^4))/4 + c
y= ln(3x^3-6) + e^(2x-5)
y'= (9x^2)/(3x^3-6) + 2e^(2x-5)
int_-2^0 (x^3+2x^2-4x) \ dx
28/3 or 9.33
Rules applied in calculus to determine derivatives of exponential, logarithmic and trigonometric functions.
Trascendental Rules of Differentiation?
The derivative of f(x)=x is...
1