Question

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 = ?

Answer #1

Consider the following.
f(x) = 4x2 + 8x − 18
(a) Find the derivative, by using the definition.
f '(x) =
(b) Find the instantaneous rate of change of the function at any
value.
f '(x) =
Find the instantaneous rate of change of the function at the
value
x = −3.
f '(−3) =
(c) Find the slope of the tangent at the value
x = −3.

Find the derivative of the function.
(a) f(x) = e^(3x)
(b) f(x) = e^(x) + x^(2)
(c) f(x) = x^(3) e^(x)
(d) f(x) = 4e^(3x + 2)
(e) f(x) = 5x^(4)e^(7x+4)
(f) f(x) = (3e^(2x))^1/4

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

1). Find the derivative of the function
f(x) = ln(x9 + 3) − 4ex/2 − x
.
2). Find the equation for the tangent line to the curve
y = f(x) at the given x-value.
f(x) = x ln(x − 5) at x = 6
.
3). Use implicit differentiation to find
dy/dx.
y2 − yex = 19
.
4). The United States population (in millions) is
predicted to be P(t) =
317e0.01t, where
t is the number of years after 2013.†...

1. Find the derivative of the function.
y = e−8/x
2. Find the derivative of the function.
s = t8et
3. Find the derivative
of the function.
y = ex5 − (ex)5
4. Find the derivative of the function.
y = e−5x ln(6x)

1. The derivative of y=e−6x+sin3xy=e−6x+sin3x is
________
2. The derivative of y=e512x+sec18xy=e512x+sec18x is
________
3. The derivative of y=x4sin8x+8xcos20xy=x4sin8x+8xcos20x is
_____
4. Find the average rate of change of the function
f(x)=x2−2f(x)=x2−2 over the interval [−2,3]
5. Find the derivative of the function y=37x3−23xy=37x3−23x when
x=8x=8.
6. Find the derivative of the function y=6x+78x+2y=6x+78x+2 at the
point (2,3)(2,3).
7. Find the derivative of the function y=4x+59x+

Given the function
h(x)=e^-x^2
Find first derivative f ‘ and second derivative
f''
Find the critical Numbers and determine the intervals
where h(x) is increasing and decreasing.
Find the point of inflection (if it exists) and determine
the intervals where h(x) concaves up and concaves
down.
Find the local Max/Min (including the
y-coordinate)

Find the derivative of the function using the definition of
derivative.
f(x) =
1
5
x −
1
6
f '(x) =
B,
f(x) =
2.5x2 − x + 4.8
f '(x)
=
C,
f(x) =
3x4
f '(x)
=
D,
If
f(t) =
3
t
and
a ≠ 0
, find f '(a).
f '(a) =

find the derivative of the function and f'(x) at x=4
f(x)= (sqrt(x)+5x) ((x^3/2)-x)

Please Find: f(x)=x2+2
1) The derivative of f(x) using the limit definition:
2) The instantaneous rate of change at x=3:
3) The equation of the tangent line at x=3:
Please write out all the steps clearly.

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