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get the first derivative of N

Initial equation - 100 +10B + 20N - B2 - N2 + 0.5 BN ( B2= B to the secondpower and N2 equals N to the second power) I want to get the first derivative of N so I got this far: 10-2b + .5n =0 .5n=2b -10 N= 4b -20. I can't figure out how they got the answer for N ? Also, why is the number 10 without the B when

Differentiation Calculation Functions

Can you please show me how to calculate the following 1. Differentiate f(x) = 1n(5x - 7) with respect to x 2. Obtain the derivative of f(t) = 1n( 5 - 2/3 t)

Derivatives of Logarithmic and Exponential Problems

Differentiate each of the following functions with respect to the appropriate variable: 1. f(x) = ln(7-5x) 2. y(x)=e^(4x-5) 3. f(x) = ln(x- 3/7 t) 4..... Please see the attached file for the fully formatted problems.

Derivatives: Relative Minimum or Maximum

Please show that the function f(x) = ln(x) does not have a relative minimum or relative maximum. Please show that for a polynomial of degree 3, if 1 + i is a zero, then 2 + i is not a zero.

Inverse functions

Please see problems and show step by step solution in detail please. --- 7.4 Inverse functions Differentiate the problems: 1) f(x) = ln(x^2 + 10) 2) f(à?) = ln(cos à?) 3) f(x) =log2(1-3x) 4) f(x) = 5thROOT(ln x) 5) f(x)=SQRTx * (ln x) 6) f(t) = ln [(2t+1)^3 / (3t-1)^4] 7) h(x)=ln(x + SQRT(x^2-1)) 8) g(x)=ln[(


1.) compute the derivative of f(x)= arctan (x^2) 2.) compute the derivative of f(x)= ln(x^2/(2+x)) 3.) determine an equation for the line tangent to the graph of y= xe^x at the point on the graph were x=2

Derivatives, maxima, minima

1. Find the derivative: f(x) = (x^3-8)^(2/3) 2. Write and equation of the tangent line to the graph of y = f(x) at the point on the graph where x has the indicated value. f(x) = (3x^2 + 5x + 4)(4x + 3), x=0 3. Find the values of any relative extrema: f(x)=1/(x^2-1)

Application Word Problem: Continuity and Derivatives

It costs Sugarco 25 cents/lb to purchase the first 100 lb of sugar 20 cents/lb to purchase the next 100 lb and 15 cents to buy each additional pound. Let f(x) be the cost of purchasing x pounds of sugar. Is f(x) continuous at all points? Are there any points where f(x) has no derivative?


Please solve and explain. Two factories are located at the coordinates (-x,0) and (x,0), with their power supply located at (o,h). Find y such that the total amount of power line from power supply to the factories is a minimum.


A rectangular package can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume. Assume cross section is square.

Maximum area with given perimeter

A Norman window is constructed by adjoining a semicircle to the top of a rectangular window. Find the dimensions of the Norman window of maximum area if the total perimeter is 16 feet.


Use a graphing utility to graph f and g in the same window and determine which is increasing at the faster rate for "large" values of x. What can you conclude about the rate of growth of the natural logarithmic function? f(x) = ln x, g(x) = the square root of x

Differentiation over Interval Values

1. Suppose f'(t) <0 for all t in the interval (2,8). Explain why f(3) > f(5) 2. Suppose f(0) = 3 and 2 is less than or equal to f'(x) which is less than or equal to 4 for all x in the interval [-5,5]. Determine the greatest and least possible values of f(2).


Find the length and width of a rectangle that has an area of 64 square feet and a minimum perimeter.

Differentiation - Point on a graph

Please solve and explain how to do so. Find the point on the graph of the function that is closest to the given point. f(x) = the square root of x Point: (4,0)

Differentiation and chemical reaction

Please solve to the specified answer and explain how to do so. In an autocatalytic chemical reaction, the product formed is a catalyst for the reaction. If Q sub zero is the amount of the original substance, and x is the amount of catalyst formed, the rate of the chemical reaction is dQ/dx = kx(qsubzero - x) For what

Inflection and concavity

Please find the points of inflection and discuss the concavity of the graph of the function. Please explain as much as possible. Please show how to obtain these answers. f(x) = x/x^2 + 1