f(x)=sin(x)
sin(x)

Plot(sin(x))

f(0)
0

f(1)
0.841470984807897

f(\pi)
0

f'(x)
cos(x)

f''(x)
-sin(x)

f'''(x)
-cos(x)

D(f(x))
cos(x)

g(x,y)=x^2+x*y+y^2
x^2+y^2+x*y

g(2,3)
19

D(g(x,y),x)
2x+y

D(g(x,y),y)
x+2y

Diff(f(x),x)
cos(x)

D(f(x),x,3)
-cos(x)

f(x)
sin(x)

scroll(a,-3,3,.01)
Plot([f(x),f(a)+f'(a)*(x-a)],x=[-3,3],y=[-3,3])

Plot([f(x),f'(x),f''(x)],x=[-3,3],y=[-3,3])

ParametricPlot([sin(7u), sin(8u)], u=[0, 2\pi,400], numbers=3, color=navyBlue)

Multiplot(plot(sin(x)),ParametricPlot([cos(t),sin(t)],t=[0,2\pi,200]))

ImplicitPlot(cos(x)+sin(y)=1, x=[-8, 8], y=[-8, 8])

ImplicitPlot(cos(x)+sin(y)=cos(T), x=[-8, 8], y=[-8, 8])

Plot(sin(x+T))

ListPlot([1,2,3,4,5],[-2.1,-1.3,.7,2.2,4.1],regression=linear)

ListPlot([1,2,3,4,5],[-2.1,-1.3,.7,2.2,4.1],regression=quadratic)

PolyFit([[1, 3], [5, 7]])
x+2

h(x)=PolyFit([[1, 3], [5, 7],[2,3]])
(x^2)/3+-x+11/3

h(1)
2.999999999999999

h(5)
6.999999999999998

h(2)
2.999999999999999

ListPlot([1,5,2],[3,7,3])

Table(sin(x),[x,0,1,.1],y)


Integrate(sin(x),x)
-cos(x)

Integrate(x^2*sin(x),x)
-1x^2*cos(x)+2x*sin(x)+2cos(x)

Integrate(exp(x)*cos(3*x),x)
(cos(3x)*exp(x))/10+(3sin(3x)*exp(x))/10

Integrate(x^2+2x*y,x)
(x^3)/3+x^2*y

Integrate(x^2+2x*y,y)
x^2*y+x*y^2

Integrate(sin(x),x,0,\pi)
2

Integrate(x^10*exp(2x),x)
(-14175x*exp(2x))/4+(-4725x^3*exp(2x))/2+(-945x^5*exp(2x))/2+-45x^7*exp(2x)+(-5x^9*exp(2x))/2+(x^10*exp(2x))/2+(45x^8*exp(2x))/4+(315x^6*exp(2x))/2+(4725x^4*exp(2x))/4+(14175exp(2x))/8+(14175x^2*exp(2x))/4

g(x,y)=x^2+x*y+2*y^2
x^2+2y^2+x*y

D(g(x,y),x)
2x+y

D(g(x,y),y)
x+4y

-D(g(x,y),x)/D(g(x,y),y)
(-2x+-y)/(x+4y)

dy(x,y)=iDiff(g(x,y),y,x)
(-2x+-y)/(x+4y)

ImplicitPlot(g(x,y)=g(1,1),x=[-4,4],y=[-4,4])

dy(1,1)
-3/5

MultiPlot(ImplicitPlot(g(x,y)=g(1,1),x=[-4,4],y=[-4,4]),Plot(1+dy(1,1)*(x-1)))

Plot(1+dy(1,1)*(x-1))

ImplicitPlot(g(x,y)=g(1,1),x=[-4,4],y=[-4,4])

ImplicitPlot(g(x,y)=g(1,1),x=[-4,4],y=[-4,4],style=Lines)