Question

Find the derivative of each of the following functions:

(a) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)

(b) y =63 (d) w=3u^(-1) (f) w=4u^(1/4)

2. Find the following:

(a) d/dx(-x^(-4)) (c) d/dw 5w^4 (e) d/du au^b

(b) d/dx 9x^(1/3) (d) d/dx cx^2 (f) d/du-au^(-b)

3. Find f? (1) and f? (2) from the following functions: Find the derivative of each of the following functions:

(c) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)

(d) y =63 (d)w=3u^(-1) (f) w=4u^(1/4)

4.

(a) y=f(x)=18x (c) f(x)=-5x^(-2) (e) f(w)=6w^(1/3)

(b) y=f(x)=cx^3 (d) f(x)=3/4x^(4/3) (f) f(w)=-3w^(-1/6)

Answer #1

Note: Please post only one question at a time.

Find the derivative of the function.
(a) f(x) = e^(3x)
(b) f(x) = e^(x) + x^(2)
(c) f(x) = x^(3) e^(x)
(d) f(x) = 4e^(3x + 2)
(e) f(x) = 5x^(4)e^(7x+4)
(f) f(x) = (3e^(2x))^1/4

Find the function whose derivative is given (i.e. solve each differential
equation). Note: E>G. Answers: A,B,D,E,F,G
a) dy/dx=6x^2. y(x)=Ax^B + C.
b) du/dt=8t(t^2 + 2). u(t)=Dt^E + Ft^G + C. ans:6

1102) a) intg{dx}=Ax+C. b) intg{x dx}=Bx^D + C. c)
intg{(1/x^2)dx}=Ex^F + C. d) intg{7x^8 dx}=Gx^H + C. Answers:
A,B,D,E,F,G,H. ans:7
1104) a) intg{4(x+8) dx}=Ax^2 + Bx + C. b) intg{(8/sqrt(2x))
dx}=Dx^E + C. Answers: A,B,D,E,F,G,H c) intg{sqrt(x)(7x-6)
dx}=(Fx+G)x^H + C. ans:7

1). Find the derivative of the function. y= 3ln(x+6)/2-6x
2). Find the derivative. y= e^x^5 ln x

Part 1) Find the derivative of the function
f(x)=e^((x^2)/(x^2+4))
Part 2) Find the derivative of the function
f(t)=(e(^t^2)+4t)^4
Part 3) Find the derivative of the function y=log6sqrt(8x+3)
Part 4)
The number x of stereo speakers a retail chain is willing to
sell per week at a price of pp dollars is given by
x=78sqrt(p+24) -390
Find the supply and instantaneous rate of change of supply when
the price is 75 dollars.
Supply = 386
Instantaneous rate of change of supply...

Please find the derivative of the following functions and show
full work:
1) f (x) = sin^3 (cos(2x))
2) y = e^cosh5x
***the cosh5x in #2 is all to the power of e.

Question 1 all parts
a)Compute the derivative dy/dx for y = 5 sqrt (8pi)+ x^6/2 +
26e^x.
b)Compute p(y)' of the function p(y)=4y-5/6y+4
c)write the equation of the tangent line to the graph y=1+9 ln x
at the point that x=1
d)determine the slope of the tangent line to the curve
2x^3+y^3+2xy=13 at the point (1,2)
e)Compute the derivative dw/dz of the function w = (37 + z sin
z)^2

Let X = {1, 2, 3} and Y = {a, b, c, d, e}.
(1) How many functions f : X → Y are there?
(2) How many injective functions f : X → Y are there?
(3) What is a if (x + 2)10 = x 10 + · · · + ax7 + · · · + 512x +
1024?

Find the derivative of the functions
y=cot-1(1/x^2+1)
y=(cos-1x)^2
y=tan-1(x^2sinx^3)
y= In(1/1+x^2)
y=(In(1+x^5))^2
y=(cos(x^2+1)^7

Find the value of the directional
derivative of the function w = f ( x , y , z ) = 2 x y + 3 y z
- 4 x z
in the direction of the vector v =
< 1 , -1 , 1 > at the point P ( 1 , 1 , 1 ) .

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