Question

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use *C* for the constant of
the antiderivative.)

1.)f(x) = 5/x^4

2.)f(t) = 2+t+t^2 / sqrt (t)

3.)f(x) = 7sqrt(x^2) + xsqrt(x)

Answer #1

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
!.) f(x) =
8x + 3
2.)f(x) =
x2 − 7x + 3
3.)f(x) =
6x5 − 4x4
− 9x2
4.)f(x) =
x(12x + 4)

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) = ⁹√x² +
x√x
F(x) =

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) = 4x
+ 7
f(x)=
Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) =
9
x8
f(x)=
f '(t) = sec(t)(sec(t) + tan(t)), −− π/ 2
< t < π/ 2 , f ( π/ 4) = −3
f(t)=
Find f. f '''(x) = cos(x), f(0)...

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) =
11x4/7 +
6x−6/7
f(x)=

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
g(x) = (7 − 6x³ + 4x⁶) /
(x⁶)
G(x) =

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
r(θ) = sec(θ)
tan(θ) − 8eθ

(a) Find the most general antiderivative of the function f(x) =
−x^ −1 + 5√ x / x 2 −=4 csc^2 x
(b) A particle is moving with the given data, where a(t) is
acceleration, v(t) is velocity and s(t) is position. Find the
position function s(t) of the particle. a(t) = 12t^ 2 − 4, v(0) =
3, s(0) = −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)

1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0
2)Find the position function if the velocity is v(t)=4sin(4t)
and s(0)=0

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

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