Question

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)

Answer #1

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)

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)

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...

1.
Differentiate the functions:
a) f(x)=tan(1/x).
b) f(x)=sin(x^2)sin^2(x).

1) Completely simplify
2) Write the expression cot( in terms of x and y only
3) If csc x = 2 and x is in Q I, determine the exact values of
sin x and cos x.
4) Use a sum to product formula to rewrite sin 2x – sin 5x as
the product of two trig functions.
Step by Step please
5) Use a product to sum formula to rewrite sin(2x) * sin(5x) as
a sum of two trig...

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).

Differentiate the following fuctions.
(a) y=arcsin(e^x)
(b) f(x)=cosh x times 4^x
(c) y= ln ((x-1)^2/(3x+1))

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

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

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)

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