A factory’s weekly production costs y and its weekly production quantity x are related by the equation y2 - 5x3 = 4, where y is in thousands of dollars and x is in thousands of units of output. Use implicit differentiation to find a formula for dy/dx, the marginal cost of production.

Q: Find dx2 by implicit differentiation, given x³ + y³ = 8. d?y dx2

A: Given that, We have to find the value of  For that simply follow the step given as below

Q: Find the derivative of the function 1 4. y= 4x +8x dy

A:

Q: Find the derivative. y = e(lnx)2

A: dydx=ddx e(lnx)2        =e(lnx)2 ddx2(ln x)         =e(lnx)2 2x

Q: Find the derivative of the function y = sech(4x − 1)

A: We use the chain rule to find the derivative.

Q: For the given function f(x), determine the equation of the tangent line at the point P(1,1) f(x) =…

A: Equation of tangent line

Q: Find the derivative of the function.

A: The given function is y=xx4+4.

Q: Find the derivative of the function. 4 y = 3x3 - 13x - x6 dy dx

A:

Q: Find the derivative of each function using implicit differentiation. 10. 3y4 + 7x = x² +y¯3 11. 2x³y…

A: The student has specifically asked for the solution to question(10) only. Hence that question is…

Q: dy for the equation Using implicit differentiation, x4 + yª = 10 is

A:

Q: Find the derivative of the function. y3 (4x* - 7x +7)* dy dx (Type an expression using x as the…

A: It is given that y=4x4-7x2+74.

Q: Find the derivative of the function y=2x.

A: Use power rule to solve this derivative. According to power rule the derivative of xn is,…

Q: Find the nth-order derivative of the function y=(3x2−2x)lnx, x>0.

A: Use the product rule

Q: Find the derivative of the function y=2x+12x−1 at x=1.

A:

Q: Using implicit differentiation, for the equation z5+y = 12 is .

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Q: Find the derivative of the function: y = tan-(– 2x + 4)

A:

Q: Suppose that x and y are related by the given equation and use implicit differentiation to determine…

A: Suppose that x and y are related by thegiven equationx5y+y5x=9we have to find dydx

Q: Find the derivative. y = In /x+7 y' = D

A:

Q: FIND THE EQUATION OF THE LINE TANGENT TO f(x)

A: Our objective is to find the equation of tangent line at a given point.

Q: Find the derivative of the function. Y=x^2e^x

A: We are given a function , Y = x2ex we are required to calculate the derivative of this function.

Q: Find the derivative of the function. f (x) = 1/ ( 1+ sec x ) 2

A: Consider the given function, fx=11+secx2 it can be also written as, fx=1+secx-2 now differentiate…

Q: Find the derivative of the function. 8 +- +/5 y= 4. dx %3D

A:

Q: Find the derivative of the function. y = 7xe−kx

A: Differentiate both sides w.r.t xUse product rule on the right side.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the point…

A:

Q: Using implicit differentiation, for the equation z5+y = 12 is

A:

Q: For the demand equation, use implicit differentiation to find  dp/dx. 17p2 + 5p + 6 = x

A: Given:

Q: Find the derivative of the function y=(x−1)(x−2)(x−3) at x=0.

A:

Q: Calculate the derivative indicated. d'y 1 + 7x2 where dx2 \x=6 Y = 2- x3

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Q: By using the "definition of the derivative" find 2 of y = v2x? dx

A:

Q: Use the definition of derivative to find the equation of line tangent to f(x) = through 2 I = 3.

A:

Q: FIND THE DERIVATIVE OF THE FUNCTIONy=0.6e to the fifth(x) degree

A: The given function "y" is shown on the white board. We need to find its derivative. Before we get…

Q: Find the derivative. y = In /x+5 y' =D

A:

Q: Find the derivative of the function. f(x) = e In( Vx + 8 f'(x) =

A: Given, f(x) = ex ln(x+8) We have the formulas d(ex)/dx = ex                       ...........(1)…

Q: Suppose that x and y are related by the given equation and use implicit differentiation to determine…

A:

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 3. y = V(4x + 3)³

A: To find the third derivative of  y=(4x+3)34⇒y=(4x+3)34 The general rule of differentiation is…

Q: Find the derivative with respect to x: y = x3- 3*

A: The given function is: y=x3.3xWe need to find the derivative of y with respect x.Recall the…

Q: The 60th derivative of x with respect to y of y = x^60 is 60!x

A:

Q: For the demand equation, use implicit differentiation to find dp/dx. (p + 5)(x + 8) = 200 dp dx

A: Given the demand equation:                                 p+5x+8=200

Q: Find the derivative of the function y = x2x+1

A: We have to find derivative of the function: y=x2x+1  In this situation we use logarithmic property…

Q: The derivative of the function y = 2* sec(x²) is:

A: I use product rule and chain rule to solve this derivative

Q: 3. y = Vx*

A:

Q: Find equation of a line tangent to the graph: f(x) = xm) at xo = 1

A:

Q: Find the derivative of the function. y = 5x 9. 3 - 13x - ヤ dx

A: y=5x3-13x-9x7

Q: Use the definition of the derivative to find the equation of the tangent line to the graph of y = Vx…

A: We write 6x+3y=4 in y=mx+b form to find slope

Q: Suppose that x and y are related by the given equation and use implicit differentiation to determine…

A:

Q: Can you help me find the fourth derivative of y=1/√x?

A: We have to find

Q: Find the equation of the tangent line at y = 0. given the inverse function x = (3y + 2)(y + 1)-.

A: Multiple of slope of line and tangent line is -1

Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line

Q: Find the derivative of the function. 4x° +8 y = y' =O

A: We have to find