Question

Diﬀerentiate the following functions. Simplify your answers. SHOW ALL STEPS.

A. h(x) = (e^3x −2)^5

B. A(x) = lnx/2x^6

Answer #1

Please thumbs up if it was helpful will be glad to know;)

Show whether the following vectors/functions form linearly
independent sets:
(a) 2 – 3x, x + 2x^2 , – x^2 + x^3
(b) cos x, e^(–ix), 3 sin x
(c) (i, 1, 2), (3, i, –2), (–7+i, 1–i, 6+2i)

1. Differentiate the following functions. Do not simplify.
(a) f(x) = x^7 tan(x)
(b) g(x) = sin(x) / 5x + ex
(c) h(x) = (x^4 + 3x^2 - 6)^5
(d) i(x) = 4e^sin(9x)
(e) j(x) = ln(x) / x5
(f) k(x) = ln(cot(x))
(g) L(x) = 4 csc^-1 (x2)
(h) m(x) = sin(x) / cosh(x)
(i) n(x) = 2 tanh^-1 (x4 + 1)

Consider the following functions
f(x) =x^2, g(x) = lnx, h(x) = cosx
For each of the following parts, you may use compositions,
products, and sums of thefunctions above, but no others. For
example, we can combine in the following waysh(g(x)) = cos(lnx), or
g(x)h(x) = lnxcosx, or g(x) +h(x) = lnx+ cosx
show how derivative rules apply to the function you came up
within order to produce the requested derivative.
1)A functionk(x) whose derivative is k′(x) = −tanx=
-(sinx/cosx)
2)...

Find the derivatives of each of the following functions. DO NOT
simplify your answers.
(a) f(x) = 103x (3x5+ x − 1)4
(b) g(x) = ln(x3 + x) /
x2 − 4
(c) h(x) = tan-1(xex)
(d) k(x) = sin(x)cos(x)

Find the derivatives of the following functions
(simplify when appropriate). Please neatly show
your work.
a. f(x)= xsin^2(x)
b. f(x)=tanh(2x)+cosh(x)+4sinh(x)
c. f(x)= tan(2x)+cos(x)+4sin(x)
d. f(x)= 2√(x)-x^(2/3). Find f'(1).

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

1. Given f(x)=2x^3-3x^2+4x+2, find (f^(-1))'(14).
Differentiate and Simplify
2. f(x)=ln(3x) e^(-x^2 ) (Answer with positive exponents
Integrate and Simplify 3. ∫▒(6x^2-5x)/√x dx

A.) Find the range of f(x) = 2x+1/x-3 show all workings. B.)
Find the range f(x)=3x-2/x-5 show all workings C.) find the range
of f(x)=1+√x+2

1- For the following functions, find all critical numbers
exactly.
f(x) = x − 2 sin x for −2π < x < 2π
f(x) = e^−x −e^−3x for x > 0
f(x) = x^5 − 2x^3

For the given functions, find y′ . You do not need to simplify
the answer.
a. f(x)=(3x^2)ln(5x+4)
b. y = e^(4x-3)/(2x^2-7)^2
(2x2 −7)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 15 minutes ago

asked 27 minutes ago

asked 36 minutes ago

asked 43 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago