Question

Generate a formula for the derivative y = log base a of x hint: use a log property. Also, how do you find a formula for the derivative?

Answer #1

Please comment if you have any doubts will clarify

4. Use the definition of the derivative to the find the
derivative . y= -x^2+3x Derivative: __________________

In class I gave a general formula for derivative of an
exponential function f(x) = loga u(x); where "a" is
called Base, and u(x) is called the argument of the log function,
which is also given below.
Note, the derivative of a logarithmic function f(x) has three
parts and is given here:
f ' (x) = 1/ln (a) . 1/u(x) . u ' (x)
In your words, describe (in words only) each one of
the three parts shown above:
a- describe...

log base 2 (x+4) + log base 2 (x+3) =1
I got solutions x=-5 and x=-2, but are both valid solutions or
just one? I checked work on an app and found the solution to be
x=-2, but i do not know how to check myself without using a
calculator.

Use the shortcut rules to mentally calculate
the derivative of the given function. HINT [See Examples 1 and 2.]
f(x) =
4x4 + 7x3
− 3
f '(x)
=
Use the shortcut rules to mentally calculate
the derivative of the given function. HINT [See Examples 1 and 2.]
f(x) = −x +
(8/x) +1
f '(x) =
Find the derivative of the function. HINT [See Examples 1 and
2.] f(x) =
8x3 − 4x2
+ x
f '(x)
=
Find...

A box with a square base and open top must have a volume of
108000 cm^3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only x, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of x.]
Simplify your formula as much as possible....

Use logarithmic differentiation to find the derivative of the
function.
(a) y = (x + 1)^(2)(x + 2)^(3)
(b) y = (x – 1)^(2)(x + 1)^(3)(x + 3)^(4)
(c) y = ex
(d) y

A box with a square base and open top must have a volume of
157216 cm3cm3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only xx, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of xx.]
Simplify your formula as much as possible....

Use logarithmic differentiation to find the derivative of the
function.
y =
sin6(x) tan2(x)
(x2 + 4)2

Use logarithmic differentiation to find the derivative of y.
y=4 square root x(x-4) over x3+4

Given y[n]=x[n]cos[(π/4)n] , Find the DTFT of y[n].
The hint we were given is to use the convolution in frequency
domain using the dirac delta function property of the cosine. i
will like if you help. Thanks

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