A factory is dumping pollutants into a river at a rate given by dx/dt = t3/4/600 tons per week, where t is the time in weeks since the dumping began and x is the number of tons of pollutants. (a) Find the equation for total tons of pollutants dumped.

Q: Can you help me with this problem step by step?

A: The logarithmic expression

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: Solve the second derivative forf(x,y, 2) = e

A: Given f(x,y,z)=esin(x²+y²)/z To find del²f/delx²

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: When a vertical beam of light passes through a transparent medium, the reason that its intensity I…

A: We have to find What is the beam intensity at 15 feet below the surface.

Q: Can you help me step by step?

A: Given function is

Q: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: part ii, thank you very much.

A:

Q: Discuss how the concept of instantaneous velocity v(t) can lead to the mathematical notion of a…

A: Topic:- application of derivatives

Q: y = kx xe

A: y=xe-kxTo solve the derivative

Q: find the derivative of the function y=-5(8x^2+7)^-6 dy/dx=___?

A: Given function is :  y = -5(8x2 + 7)-6

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

A: on doing differentiation we get

Q: Find the derivative of the function f(x)=ln(10e^13x−7).

A: Note: Since you didn't use parenthesis while writing the function, there can be two possibilities…

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: find the derivative. y = ln(t5t )

A:

Q: A town library estimates that, when the population is x thousand persons, approximately y thousand…

A: A town library estimates that, when the population is x thousand persons, approximately y thousand…

Q: Find the first derivative of: x = t²e2t

A:

Q: find dy / dx by implicit differentiation.

A: We have to find dydx by implicit differentiation: x5+y5=16 We know the formula of differentiation,…

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x'-5x)* 1. y= d'y/dx'

A:

Q: The rate at which the number of bacteria in a culture is changing (in thousands of bacteria per…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: - [5√3x d dx

A:

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: 14. The first derivative of y = arcsin4x is а. -4 b. -4 C. d. V1- 16x? VI- 4x2 V1– 16x? /1– 4x* -

A:

Q: _xe. f(x) = (1+e*)

A: Here we have to find the differentiation of given function. The solution is following.

Q: Find dy/dx by implicit differentiation. x5 + y5 = 16

A: To Determine: Find dy/dx by implicit differentiation. x5 + y5 = 16 Given: we have x5+y5=16…

Q: Can you help me step by step with this problem?

A: Obtain the derivative of the given function as follows.

Q: Find the indicated derivative. 1 - 2x2 x4 - 2x2 + 4 dy for y dx dy dx %3D

A: We will find dy/dx, using the form of             d/dx (u/v) .

Q: Find the derivative of the function. y=-6(8x+8)-6 dy/dx=

A:

Q: Find the derivative d (2* log2 x) dx

A:

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: The number of hours of skilled labor is y and unskilled labor is x.

Q: Solve for the derivative of y IMPLICITLY 22 + Væ3 + 2y= y²

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: Why is the notation dy/dx used to represent the derivative?

A:

Q: Find the indicated derivative. dy for y = 1- 2x2 x4 - 2x2 dx + 3 dy dx

A: Quotient rule: ddxuv=vddx(u)-uddx(v)v2

Q: - In y = e' sin x

A: We have to find dy/dx of the above equation.

Q: Find the first derivative. (a) y=x* (b) y =xnx 2.

A:

Q: (b). Find the second derivative. y=x²-5vx

A:

Q: Find the derivative of the function. y= -3(6x2 +8) -6 dy dx (Type an expression using x as the…

A:

Q: Find the derivative of the function. y = 5 e - 5x+1 dy dx

A: Note:- Answer is given in the picture

Q: -2(х-1 — х?) dx

A:

Q: Find the derivative. 4 dx dx

A: Explanation: Given that,  ddxx6-4x

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x³-5x)* 1. у3D ; d'y/dx³

A:

Q: j. y=5 ln (x² +4)

A:

Q: Find the derivative of F(x) = t°e' ln tdt.

A:

Q: Find the value of the derivative. dy if y = 3 - 7x2 dx |x = - 3 dy (Simplify your answer.) %3D dx |x…

A: y=3-7x2dydx=0-14x       =-14x

Q: (2x + 1) 2 dy dx |- 2x

A:

Q: Find the derivative y=ln(t2)-arctan(t/4) y'=?

A: Given, y=ln(t2)-arctan(t/4) y'=?

Q: Find the derivative of the function f(x) = 3 ln(x) + e5ª. df = dx

A:

Q: Find the indicated derivative. 1- 2x2 x4 - 2x2 + 3 dy -for y = dx dy dx

A: Recall: uv'=vu'-uv'v2

Q: Find the derivative.  y = ln((x + 1)(2x + 9))

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.