The monthly output of a certain product is Q(x) = 1200x5/2 where x is the capital investment in millions of dollars. Find dQ/dx, which can be used to estimate the effect on the output if an additional capital investment of $1 million is made. dQ/dx =

Q: Find d2y/dx2 by implicit differentiation x3 + y3 = 1

A:

Q: Find dy/dx by implicit differentiation.

A: To find: The derivative of x3y-xy3=4. Concept used: Chain rule of derivative: fgx'=f'gx·fgx Product…

Q: 3 dx|

A:

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. у 3 ; d'y/dx

A: Question 1,Given,            y=x2-3x3xTo find : d3ydx3

Q: Find  dy dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: tan−1(4x2y) = x + 5xy2 We differentiate both sides with respect to x using the product rule and…

Q: part ii, thank you very much.

A:

Q: Find the indicated derivative. for y = dx 1 - 2x2 x* - 2x2 + 3 dy dx II

A: on doing differentiation we get

Q: find derivative d/dx ln(3x/(2x+7)^1/2)

A:

Q: by implicit differentiation. dx Find - (5x + 2y)1/3 = x2 dx

A:

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

A:

Q: Find dy/dx by implicit differentiation X2 + 4xy - y3 =6

A:

Q: Find by implicit differentiation. dx x - y = 6x 3x + 10y dy dx

A:

Q: Find the derivative of the function.

A: Given y=lnx+1x-1

Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

A:

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: find dy / dx by implicit differentiation.

A:

Q: Find the anti-derivative of: S(3x* – 6x)° (2x³ – 1)dx

A:

Q: Find dy/dx by implicit differentiation   x2 + 5x + 9xy - y2=4

A:

Q: Find the derivative of y with respect to the independent variable. x2 y =log 8 Sx+1 1 8x+1 O In8 x2…

A:

Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

A:

Q: Calculate the second derivative y : Vx - /y = 1

A:

Q: Integrate sec√x dx ÷ √x

A: We have to Integrate : ∫secxxdx Let x=t⇒12xdx=dt⇒dx=2xdt=2t dt Now, ∫secxxdx=∫sec tt(2t dt)=∫2 sec t…

Q: Find dy/dx by implicit differentiation. x²y³ -yax dy/dx =

A:

Q: find dy/dx by implicit differentiation x3 + 4xy - 3y4/3 = 2x

A: Given: x3 + 4xy - 3y4/3 = 2x

Q: Find the given derivative 6 Dx 7x 1 Dx 7x 5 LN +

A:

Q: Find dy/dx by implicit differentiation. x4y6 - 24xy4 = 22

A:

Q: Calculate the derivative.

A:

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

Q: Integrate ∫(ln(x))/x

A: We need to integrate the given logarithm function:

Q: Find dy/dx by implicit differentiation. x2y3 − 12xy2 = 6

A: To determine the implicit derivative.

Q: Calculate the derivative. 3 y = log 3X y' =D

A:

Q: Find dy/dx by implicit differentiation. x3 + 7x + 3xy - y5 = 25

A:

Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

A:

Q: 2. Use Logarithmic Differentiation to find dy/dx for y = 3 x(2x+5) (x²+1)²

A: Explanation of the answer is as follows

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

A:

Q: Find the given derivative. DX 5x -- Dx 5x 1/3 1/3

A:

Q: Differentiate the function. y=ln(x5sin2x)

A: Given function:

Q: f y = (sin x)x b

A:

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: The derivative of the function y = cos(x ln 3)log3 (sin x) is:

A:

Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

Q: Find dy/dx by implicit differentiation at point (0,-2) if x^3-xy+y^2=4. O -2 -2/3 1/2 3/4

A: Implicit derivative at point

Q: Find dx by implicit differentiation. y = 5x + 6yx

A:

Q: Find dx * by implicit differentiation. r+y+ 4

A: x+y+xy=4d(x+y)dx+d(xy)dx=d(4)dx

Q: Find the derivative of the function. y = log |5- 2x dy dx

A:

Q: differentiation

A:

Q: What is the integrating factor of y' - 2xy x?

A:

Q: 3. Use logarithmic differentiation to find the derivative of the function. (2x – 1) Vx+1 y =

A: giveny=(2x2-1)5x+13taking log on both sidelogy=log(2x2-1)5x+13using log…