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Calc 1 2.5

 

<== Calculus 1
Number Question Answer
See the work

1.

 

 

 

Let 

ƒ(x)=sqrt(4x^2+3x+2)

ƒ'(x)=_______
ƒ'(1)=_______ 

 

ƒ'(x)=(0.5*(4*x^2+3*x+2)^(-0.5))*(8*x+3)                      
ƒ'(1)=11/6
The work

Point Cost: 3

2.

 

 

 

Let 

ƒ(x)=(x^3+2x+5)^2

ƒ'(x)=_______

 

ƒ'(x)=(2*(x^3+2*x+5))*(3*x^2+2)

 

The work

Point Cost: 3

 

3.

 

 

 

Let 

ƒ(x)=(3x+8)^-3

ƒ'(x)=_____
ƒ'(5)=_____ 

 

ƒ'(x)= (-3*(3*x+8)^(-4))*(3)
ƒ'(5)= -3.22*10^-5
The work

Point Cost: 3

4.

 

 

 

Suppose that

y=(2.2x^2+3.7)^(1/5)             

Find dy/dx.

 

dy/dx=((2*2.2*x)/5)*(2.2*x^2+3.7)^(-4/5 )

 

The work

Point Cost: 3

 

5.

 

Suppose that

y = (-4)/(6x^2+4x-4)

Find dy/dx.

 

 

dy/dx=(4)*(2*6*x+4)(6*x^2+4*x-4)^(-2)

 

The work

Point Cost: 3

6.

 

 

 

Let

ƒ(x)= sin(6x+6)

ƒ'(x)=

 

ƒ'(x)= 6cos(6x+6)

 

The work

Point Cost: 1

 

7.

 

 

Let ƒ(x)= -4(cos(x))^4

ƒ'(x)=

 

ƒ'(x)= 16(cos(x))^(3)(sin(x)) 

 

The work

Point Cost: 2

 

8.

 

 

 

Let ƒ(x)= sin(x^2)

ƒ'(x)=_____

ƒ'(1)=_____

 

ƒ'(x)= (cos(x^2))(2x)

ƒ'(1)= 1.0806

 

The work

Point Cost: 3

9.

 

 

 

Let

ƒ(x)= -3csc(3x)

ƒ'(x)=_____

 

ƒ'(x)= 9/(tan(3x)sin(3x))
The work

Point Cost: 3

10.

 

 

 

Let

ƒ(x)= -8cos(cos(x))

ƒ'(x)=_____

 

ƒ'(x)= -8sin(cos(x))sin(x)
The work

Point Cost: 2

11.

 

 

Let ƒ(x)= 8cos(cos(x^8))

ƒ'(x)=______

 

ƒ'(x)=  64x^(7)*sin(cos(x^(8)))*sin(x^(8))

 

The work

Point Cost: 2

12.

 

 

 

Let

s(t)=((t^8+1)/(t^8-1))^(1/5)

s'(t)=_______

 

s'(t)= 1/5((t^(8)+1)/(t^(8)-1))^(-4/5)*(-16t^(7))/(t^(8)-1)       
The work

Point Cost: 3

13.

 

 

 

Let

y= (7+cos^2(x))^11

dy/dx= __________

 

dy/dx= -2cos(x)sin(x)*11(7+(cos(x))^2)^(10)

 

The work

Point Cost: 3

 

14.

 

 

 

 

Find an equation of the tangent line to the curve     

y= sin(7x)+cos(2x)

at the point (π/6, y(π/6)). Tangent line:

y=________

 

y= sin(7π/6)+cos(2π/6)+(7cos(7π/6)-2sin(2π/6))*(x-π/6)
The work

Point Cost: 3

15.

 

 

 

 

 

 

A table of values for ƒ, g, ƒ', and g' is given below.     

x f(x) g(x) f'(x) g'(x)
 1  3 1 3 3
 2 2 3 2 2
 3 2 1 3 2

(A) If h(x)=ƒ(g(x)), then h'(3)=______

(B) If H(x)=g(ƒ(x)), then H'(3)=_____

 

A= 6

B= 6

The work

Point Cost: 3

16.

 

 

 

 

Suppose that

ƒ(x)= (3x)/(4-3x)^5

Find an equation for the tangent line to the
graph of ƒ at x=2

Tangent line: y=_______

 

y= 1/3125(x-2)-0.1875

 

The work

Point Cost: 4