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Calc 1 2.4

 

<== Calculus 1
Number Question Answer
See the work

1.

 

 

 

Let 

ƒ(x)=x^3cosx

ƒ'(x)=_______ 

 

ƒ'(x) = ƒ'(x)=3x^(2)*cos(x)-x^(3)*sin(x)                      

The work

Point Cost: 3

2.

 

 

 

Let 

ƒ(x)=(4x-6x^3)(7+sqrt(x))

ƒ'(x)=_______

 

ƒ'(x) = ƒ'(x)=(4-18*(x)^2)*(7+sqrt(x))+(4*x-6*x^3)*(1/(2*sqrt(x)))

 

The work

Point Cost: 3

 

3.

 

 

 

If 

ƒ(x)= cos(x)-5tan(x), then

ƒ'(x)=_____

 

ƒ'(x) = -sin(x)-5(sec(x))^2
The work

Point Cost: 3

4.

 

 

 

If ƒ(t)=(t^2+5t+8)(5t^(-2)+3t^(-3))       

Find ƒ'(t).

 

ƒ'(t) = (2t+5)*(5t^(-2)+3t^(-3))+(t^2+5t+8)*(-10t^(-3)-9t^(-4))          

 

The work

Point Cost: 3

 

5.

 

 

 

If

Find ƒ'(x):

Find ƒ'(4):

 

 

Find ƒ'(x)= 0

Find ƒ'(4)= 0

 

 

The work

Point Cost: 2

6.

 

 

 

 

If

ƒ(x)= (sqrt(x)-6)/(sqrt(x)+6)

Find ƒ'(x):

Find ƒ'(5):

 

Find ƒ'(x):  (6/sqrt(x))/((sqrt(x)+6)^2)

Find ƒ'(5): 0.0395572783485844

The work

Point Cost: 4

7.

 

 

 

If

ƒ(x)= (5sin(x))/(1+cosx)

then ƒ'(x)=_______

 

ƒ'(x)= (5cos(x)+5)/(1+cos(x))^2
The work

Point Cost: 3

8.

 

 

 

 

Let

ƒ(x)= 11x(sin(x)+cos(x))

ƒ'(x)=_______

ƒ'(π/4)= ______

 

ƒ'(x)= (11*(sin(x)+cos(x))+ 11x(cos(x)-sin(x)))

ƒ'(π/4)= -12.2179280799355

The work

Point Cost: 3

9.

 

 

 

If ƒ(x)=5xsin(x)cos(x),

Find ƒ'(x)

Find ƒ'(1)

 

Find ƒ'(x)= 5(sin(x)cos(x)+x(cos(x)cos(x)-sin(x)sin(x)))

Find ƒ'(1)= 0.192509384328493

 

The work

Point Cost: 3

10.

 

 

 

 

If 

ƒ(x)= (5x^2(tanx))/(secx)

Find ƒ'(x): 

Find ƒ'(5): 

 

Find ƒ'(x)=  5(2xsin(x)+x^(2)cos(x))

Find ƒ'(5)= -12.4884405502536

The work

Point Cost: 4

11.

 

 

 

Find an equation for the line tangent to the graph of


ƒ(x)= sqrt(x)/(4x-6) at the point (3, ƒ(3)).

y=_____

 

y= 0.288675134594813 - 0.144337567297406*(x-3)

 

 

The work

Point Cost: 4

12.

 

 

Let ƒ(x)= 5secx

Then ƒ''(π/9) is:

 

ƒ''(π/9)= 6.73065125171278
The work

Point Cost: 3