Question

Find the derivatives of each of the following functions. DO NOT
simplify your answers.

(a) f(x) = 10^{3x} (3x^{5}+ x − 1)^{4}

(b) g(x) = ln(x^{3} + x) **/**
x^{2} − 4

(c) h(x) = tan^{-1}(xe^{x})

(d) k(x) = sin(x)^{cos(x)}

Answer #1

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)

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).

Find the derivative of each of the functions below. Please use
proper notation for derivatives. Do not simplify your answer.
1. R(x)=-4x-2+(2/x2)-ln(x+1)+4
2. h(x)= -(4x2-x+3)23
3. q(x)=e(2x^4)-1
4. f(x)= (4x2-9x+1)(-x+ex)
5. M(x)= (4x3-x)/(x+2)

Differentiate the following functions. Do not simplify
k(x) = ln(cot(x))
L `(x) = 4 csc-1(x2)
m(x) = sin(x) / cosh(x)
n(x) = 2 tanh-1(x4 + 1)

1). Use the techniques of differentiation to find the
derivatives of the following functions
a). f(x)= (2 sqrt x + 1) (2-x/x^2+3x)
b). f(x)= cos^2 (3 sqrt x)
c). f(x) = Sin x/(x^2 + sin x)

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

13. Consider
f(x)=sqrt x-2
a) Using any of the three limit formulas to find f ′ ( a
), what is the slope of the tangent line to f ( x )at x = 18? (6
points execution, 2 points notation)
b) Find the equation of the tangent line at x =
18
14. State the derivative.
a) d/ d x [ x ^n ]
b) d /d x [ cos x ]
c) d /d x [ csc...

1a.
Find the domain and range of the function. (Enter your answer
using interval notation.)
f(x) = −|x + 8|
domain=
range=
1b.
Consider the following function. Find the composite
functions
f ∘ g
and
g ∘ f.
Find the domain of each composite function. (Enter your domains
using interval notation.)
f(x) =
x − 3
g(x) = x2
(f ∘ g)(x)=
domain =
(g ∘ f)(x) =
domain
are the two functions equal?
y
n
1c.
Convert the radian...

Using Leibniz notation (i.e., ??/??, ??/??, etc.), find
derivatives for each of the following functions. You should always
use proper notation. Your answers must be simplified.
a) ?=(3√p/(p√p))^−2
b) ?(?)=cos?/(5?^? +2tan(?))
c) ?=sin^−1((sqrt?+1))
d) ℎ(?)=?^2?^(?3)
e) ?(?)=cot^−1(?)+cot^(−1)(1/?)

1.
Calculate the following derivatives
(a) f′(x) where f(x) = e^2x sin(3x)
(b) g′(3π/4) where g(x) = sec(x) (simplify)

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