Question

Find the derivative of the given expression. f(x)=17x^2+ln(x^3)

f'(x)=

Solve the following equation for x:

ln(x−4)+ln(x−2)=ln(8)ln(x−4)+ln(x−2)=ln(8)

If more than one solution exists, separate your answers with a comma.

Answer #1

i)

we have

ii)

but x = 0 not possible,

Find the derivative of f(x) = 3^(x ln x) and f(x) = ln( 1/ x ) +
1/ ln x

1. Solve the equation ln(x + 5) − ln(x − 3) = 1 for x.
2.Find all values of x for which the following function has a
tangent line of slope 0 (i.e. f 0 (x) = 0). f(x) = e^2x+1 (2x +
5)
3.Calculate limx→−5 1 − √ x + 6/x + 5

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.†...

Find the derivative of the function.
(a) f(x) = ln (x) + 6x^(2) – 5
(b) f(x) = ln (x + 1)
(c) f(x) = 5 ln x
(d) f(x) = ln(x^(3) – 5x^(2) – 2x + 5)
(e) 2lnx / x
(f) x^(2) ln x

Find the area enclosed by y=ln(x−8) and y=(ln(x−8))^(2).
(Use symbolic notation and fractions where needed.)
A=

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

Given the polynomial f(x) = 3x^4 -7x^3 -3x^2 + 17x + 10, and
given the zeros of -1 and -2/3,
A). Write the polynomial in linear and irreducible quadratic
factors
B). Write the linear factorization of the polynomial.

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)

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)

Find the derivative of the following functions
(a) f(x) = ln(√x3 −2x)
(b) g(x) =√x2 + 3 x3 −5x + 1
.

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