Question

1. Find the derivative of

f(x)= √4-sin(x)/3-cos(x)

2. Find the derivative of

1/(x^2-sec(8x^2-8))^2

Answer #1

f(x) = (sin x)2(cos
x)5
a) Find the first derivative of your function in fully factored
form
b) Find the critical numbers over the domain
c) Find the exact slope of the tangent to your function at x=
4
d) Find the exact equation of the tangent to your function at x=
4 in slope y intercept form

[2 marks] Find the derivative of y =
√
4 sin x + 6
at x = 0.
Consider the following statements. The limit
lim
x→0
g(4 + h) − g(4)
h
is equivalent to:
(i) The derivative of g(x) at x =
h
(ii) The derivative of g(x + 4) at x
= 0
(iii) The derivative of g(−x) at x
= −4
Determine which of the above statements are True (1) or False
(2).
If f (3) = ...

Part 1) Find the derivative of the function
f(x)=e^((x^2)/(x^2+4))
Part 2) Find the derivative of the function
f(t)=(e(^t^2)+4t)^4
Part 3) Find the derivative of the function y=log6sqrt(8x+3)
Part 4)
The number x of stereo speakers a retail chain is willing to
sell per week at a price of pp dollars is given by
x=78sqrt(p+24) -390
Find the supply and instantaneous rate of change of supply when
the price is 75 dollars.
Supply = 386
Instantaneous rate of change of supply...

Find the derivative of the functionf(x) =sin(sin(cos(sin(x))))by
repeatedlyapplying the chain rule.

1. Let ?(?)=8(sin(?))? find f′(2).
2. Let ?(?)=3?sin−1(?) find f′(x) and f'(0.6).

f(x) = − cos(x^2 ) + 2 sin(x) [1,3.5]
1) find f'(x) and the roots on the given interval.
2) find all critical points of f(x) on the given interval.
3) find absolute max and min of f(x) on the given interval.

Find f.
a. f '''(x) = cos x, f(0) = 1, f '(0) = 4, f ''(0) = 3
b. f''(x) = sin(x) + cos (x), f(0) = 1, f'(0) = 3.

1. If f(x) = ∫10/x t^3 dt then: f′(x)= ? and f′(6)= ?
2. If f(x)=∫x^2/1 t^3dt t then f′(x)= ?
3. If f(x)=∫x3/−4 sqrt(t^2+2)dt then f′(x)= ?
4. Use part I of the Fundamental Theorem of Calculus to find the
derivative of h(x)=∫sin(x)/−2 (cos(t^3)+t)dt. what is h′(x)= ?
5. Find the derivative of the following function:
F(x)=∫1/sqrt(x) s^2/ (1+ 5s^4) ds using the appropriate form of the
Fundamental Theorem of Calculus.
F′(x)= ?
6. Find the definitive integral: ∫8/5...

find the derivative of the functions
T(theta)=cos(theta^2 + 3theta - 10)
f(x)=(3x/(x^2-1))^3/2

Consider f(x) = x2 – 8x. Find its derivative using
the limit definition of the derivative. Simplify all
steps.
a. Find f(x + h).
____________
b. Find f(x + h) – f(x).
____________
c. Find [f(x + h) – f(x)] ÷ h.
____________
d. Find lim (hà0) [f(x + h) – f(x)] ÷ h.
____________
e. Find an equation of the line tangent to
the graph of y = x2 – 8x where x = -3. Present your
answer...

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