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Calc 1 3.3

 

<== Calculus 1
Number Question Answer
See the work

1.

 

Let
ƒ(x)= ln(x^7)
ƒ'(x)=_____
 ƒ'(e^2) =____

ƒ'(x)=7/x
ƒ'(e^2) =0.947346983
The work

Point Cost: 1

2.

 

Let
ƒ(x)= (ln x)^3
ƒ'(x)=____
ƒ'(e^2)=____

ƒ'(x)=(3/x) *(ln(x))ˆ(2)
ƒ'(e^2)= 1.6240234
The work

Point Cost: 2

3.

 

Suppose that

Find ƒ'(1).
ƒ'(1)=________

ƒ'(1)= -0.780513367877103
The work

Point Cost: 1

4.

 

Suppose that ƒ(x)=xln(x)-x. Find ƒ '(4).
ƒ'(4)=_____

ƒ'(4)= 1.38629436111989
The work

Point Cost: 1

5.

 

Let

ƒ'(x)=_____

ƒ'(x)=
The work

Point Cost: 2

6.

 

Suppose that

Find ƒ'(2).
ƒ'(2)=____

ƒ'(2)=0.443906166427373
The work

Point Cost: 2

7.

 

Let

ƒ'(x)=_____

ƒ'(x)=
The work

Point Cost: 2

8.

 

Find the derivative of the function

g'(x)=______

g'(x)=
The work

Point Cost: 2

9.

 

Find the derivative of the function

g'(x)=______

g'(x)=
The work

Point Cost: 2

10.

 

Suppose that

Find ƒ'(1).
ƒ'(1)=______

ƒ'(1)= 0.117114183085537
The work

Point Cost: 2

11.

 

Suppose that . Find ƒ'(3).
ƒ'(3)=_____

ƒ'(3)= 51.6279179144623
The work

Point Cost: 1

12.

 

Let

ƒ'(x)=______

ƒ'(x)=
The work

Point Cost: 2

13.

If , find ƒ'(x).

The work

Point Cost: 2

14.

If , find ƒ'(x).

The work

Point Cost: 3

15.

 

Let

dy/dx=______
The work

Point Cost: 2

16.

 

Let

dy/dx =______
dy/dx =
The work

Point Cost: 2

17.

 

Let

dy/dt =_______
dy/dt =
The work

Point Cost: 2
18. Let
ƒ'(x)=______
The work

Point Cost: 2

19.

 

If ,
Find ƒ'(x)_____
Find ƒ'(3)_____

Find ƒ'(x) =
Find ƒ'(3)= 3.57796927795363
The work

Point Cost: 2

20.

 

If y= 9xln(x), find the following.
y'=_____
y''=_____

y'= 9ln(x)+9
y''= 9/x

The work

Point Cost: 1

21.

 

Let
ƒ(x)= 4ln[sec(x)+tan(x)]
ƒ''(x) =_______
ƒ''=4*sec(x)*tan(x)
The work

Point Cost: 3

22.

 

 

Find an equation for the line tangent to the graph of

at the point (a, ƒ(a)) for a= 1.
y=

y=-5.43656 - 10.8731*(x-1)

The work

Point Cost: 3

23.

 

 

Find an equation of the tangent line to the curve

at the point (2,49)
Tangent line: y=_____
y=49+95.3495973037104*(x-2)
The work

Point Cost: 2

24.

 

 

Suppose that

Find ƒ'(x), and the domain of ƒ .
ƒ'(x)=______
Domain=_______
ƒ'(x) =
Domain=(0,e^(-6)/7)U(e^(-6)/7,∞)
The work

Point Cost: 3

25.

 

 

Let

Use logarithmic differentiation to determine the derivative.
ƒ'(x)=_______
ƒ'(1)=_______
ƒ'(x)=
ƒ'(1)=4
The work

Point Cost: 2
26. If , find ƒ'(10). ƒ'(10)= 647.036555139427
The work

Point Cost: 3

27.

 

Let

Determine the derivative y' at the point (1,0).
y'(1)=____

y'(1)=2
The work

Point Cost: 4