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Copy/Paste Formulae for Chapter 17 Differentiation and antidifferentiation

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Handy Shortcuts

Shift+Enter to execute a command
Ctrl-s save your file
Alt+7 to start a text cell
Ctrl-/ gives a fraction (□/□)
Ctrl-2 gives a square root sign (Sqrt[□])
Ctrl-6 gives an exponent (□^□)

All Mathematica commands start with a Capital and use square brackets [ ]
For examples Plot [ ]

MATHEMATICA COMMANDS FOR Chapter 17

1. Instantaneous Rate of Change

D[function,x]/.x->"Enter x value here"//N

D[(x-2)/x,x]/.x->4//N

2. Average Rate of Change, Gradient of secant

c[x_]:=function
DifferenceQuotient[c[x],{x,"Enter Higher value here"-"Enter Lower value here"}]/.x->"Enter Lower value here"//N//TraditionalForm

c[x_]:=x^(-2)
DifferenceQuotient[c[x],{x,1+h-1}]/.x->1//N//TraditionalForm

c[t_]:=3*t^2+4t+2
DifferenceQuotient[c[t],{t,3-1}]/.t->1//N

3. Find the gradient of the tangent at a point

f[x_]:=function
f'["Enter x value here"]

f[x_]:=(x^2)-2x+1
f'[0]

4. Find Derivative of a function

f[x_]:=function
f'[x]//TraditionalForm

f[x_]:=Sin[x]
f'[x]//TraditionalForm

5. Limits and  Derivatives of functions

f[x_]:=function
Limit[((f[x+h]-f[x])/h),h->0,Analytic->True]//Expand

f[x_]:=x^2
Limit[((f[x+h]-f[x])/h),h->0,Analytic->True]//Expand

6. To plot one graph

Plot[{"function"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{2^x},{x,0,10},PlotLegends->"Expressions"]

7. To plot Graphs of Derivative Functions

Plot["function"&&2≤x≤5,{x,"Minimum","Maximum"},PlotRange->5]

Plot[(((x-2))^2)&&2≤x≤5,{x,0,5},PlotRange->5]

Plot[(x-2)(x-3)(x+2)&&-2≤x≤5,{x,-5,5}]

8. To plot few graphs on the same plane

Plot[{"function1","function2","function3"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{Sin[x],Sin[2x],Sin[3x]},{x,0,2Pi},PlotLegends->"Expressions"]

9. Solve Equations

Solve["Left side of Equation"=="Right side of Equation","solve for"]

Solve[2x==8,x]//N

10. Solve Simultaneous Equations

Solve[{equation here number one,another equation here},{variable1,variable2}]

Solve[{2x+3y==6,x-2y==4},{x,y}]//N

11. Simplify Expression

Simplify["Enter Expression here"]

Simplify[(((((3+h))^2)-2(3+h)-3)/(3+h-3))]

12. Plot Graphs of derivative functions with decreasing increasing and stationary signs

f[x_]:="Enter right side of the function here"
Show[{Plot[f[x],{x,"Minimum x value for the graph","Maximum x value for the graph"},PlotStyle->Black],NumberLinePlot[{f'[x]>0,f'[x]<0,f'[x]==0},{x,"Minimum x value for the graph","Maximum x value for the graph"},PlotStyle->{Red,Blue,Black},Spacings->0,PlotLegends->{"Increasing","Decreasing","Stationary"}]}]

f[x_]:=2(x^3)+3(x^2)-12x+5
Show[{Plot[f[x],{x,-3,3},PlotStyle->Black],NumberLinePlot[{f'[x]>0,f'[x]<0,f'[x]==0},{x,-3,3},PlotStyle->{Red,Blue,Black},Spacings->0,PlotLegends->{"Increasing","Decreasing","Stationary"}]}]