Skill Quiz on Differentiation

Combined Rules & Different Letters

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=Exp[5 (x^3)] = (e^(5 (x^3)))

Solution

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

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

WalkD[y, x]

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

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

(dy/dx) =

2

y =  (3^x)

Solution

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

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

WalkD[y, x]

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

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

(dy/dx) =

3

y=(e^t) Log[(t^6)]

Solution

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

\(Clear[t, y]; 
y = E\^t\ Log[t\^6]\)

WalkD[y, t]

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

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

(dy/dt) =

4

v = (u^3) Sin[(u^2)]

Solution

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

Clear[u, v]; v = (u^3) Sin[(u^2)];

WalkD[v, u]

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

    Print[\*""\!\(\[DifferentialD]v\/\[DifferentialD]u\)= "", D[v, u]]; 
    \)

(dv/du) =