Skill Quiz on Differentiation

The Chain Rule

Given:  y = f[x]

Compute : (dy/(d x))=f'[x]

Check your work

to check your work:

1)  Open Help in Mathematica (upper right of toolbar).

2)  Click Getting Started/Demos and continue selecting inside this as follows
	Demos
		Notebook Demos
			Step-by-step Differentiation (it's way down the list)
			
Run the first example in there and say "yes" to "Evaluate Initialization?"  This loads the WalkD[y,x] function so it's ready to use to check your work.

1

y = Cos[5 (x^3)]

Solution

NOTE: Read the instructions above under "Check your work" before entering the WalkD[.,.] commands below.

\(Clear[x, y]; 
y = Cos[5\ x\^3]; \)

WalkD[y, x]

\(Print[" y= ", y]; 

    Print[\*""\!\(\[DifferentialD]y\/\[DifferentialD]x\)= "", D[y, x]]; 
    \)

(dy/dx) =

2

y =  3 Log[x (Sqrt[ x]) ]

Solution

NOTE: Read the instructions above under "Check your work" before entering the WalkD[.,.] commands below.

\(Clear[x, y]; 
y = \ 3\ Log[x \@ x\ ]; \)

WalkD[y, x]

\(Print[" y= ", y]; 

    Print[\*""\!\(\[DifferentialD]y\/\[DifferentialD]x\)= "", D[y, x]]; 
    \)

(dy/dx) =

3

y = π Sin[(e^x) ] +  3 Cos[Log[x]]

Solution

NOTE: Read the instructions above under "Check your work" before entering the WalkD[.,.] commands below.

\(Clear[x, y]; 
y = π\ Sin[E\^x\ ] + \ 3\ Cos[Log[x]]; 
    \)

WalkD[y, x]

\(Print[" y= ", y]; 

    Print[\*""\!\(\[DifferentialD]y\/\[DifferentialD]x\)= "", D[y, x]]; 
    \)

(dy/dx) =

4

y = Cos[3 (x^2)  + 2 (x^3) Sin[x]]

Solution

NOTE: Read the instructions above under "Check your work" before entering the WalkD[.,.] commands below.

\(Clear[x, y]; 
y = Cos[3\ x\^2\  + 2\ x\^3\ Sin[x]]; \)

WalkD[y, x]

\(Print[" y= ", y]; 

    Print[\*""\!\(\[DifferentialD]y\/\[DifferentialD]x\)= "", D[y, x]]; 
    \)

(dy/dx) =