dium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 5 mm. V'(5) = mm3/mm What does V'(5) mean in this situation? V'(5) represents the rate at which the volume is increasing with respect to the side length as V reaches 15 mm3.V'(5) represents the volume as the side length reaches 5 mm.     V'(5) represents the rate at which the volume is increasing as x reaches 15 mm.V'(5) represents the rate at which the side length is increasing with respect to the volume as x reaches 5 mm.V'(5) represents

Q: Economists have considered the output y of a manuracturing process as a function of the size of the…

A: Derivative of function

Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: In y = 22 cosh1 2x

A:

Q: Find the derivative of the function y = ln(tanh x/2)

A:

Q: 3) Find the second derivative of y with reference to x. xcosy = y

A:

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

A:

Q: find nth derivative of y=x/(x+1)^4

A: To find the nth derivative of the function y=x(x+1)4=x+1-1(x+1)4=1(x+1)3-1(x+1)4

Q: Find the first derivative of y = (ln x)4

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

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A:

Q: Use differentials to approximate the quantity   √17

A:

Q: (a) Find the average rate of change of f(x) from x = 1 to x = 2. 7 (b) Using the definition of the…

A:

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

A:

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: SW Solve for the first derivative of ,(x+5) x' +e x³ +e + Vx f (x) = V0.1 at x= 0.05 using FCD BCD…

A: f'(0.05)=336.6222-333.90350.008=2.71870.008=339.8375 App value of f'=339.8375 exact value of…

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

A:

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: 13. Find the second derivative y “ of y = 5z2 +sinrcosz

A:

Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (3te-t)

A: We expand the function using the properties of logarithm

Q: Find the derivative of the function f(x) = ln(sinh x)

A:

Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: Find the derivative of z=(ln5)e^x dz/dx=

A:

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: What is the derivative of: y ln x − x ln y = 1

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Q: 5. First compute the derivative of f(x)= Vĩ and then use it to: a. Find the equation of the tangent…

A: Given equation of curve is fx=x. Power rule of differentiation states that: ddxxn=nxn-1…

Q: This is determined by the largest derivative, or the highest level of differentiation, present in a…

A: We have to check

Q: What is the first derivative of the expression (xy)× = e?

A: See the details solution in below

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A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: find the derivative of y with respect to the givenindependent variable. y = 3 log8 (log2 t)

A:

Q: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A:

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A:

Q: Find the derivative of the function y, below. y = 2x(ln x + ln 5) – 9x + v2 dy dz ||

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log4 x + log4 x2

A: Given: By using logarithm base change rule, the function can be rewritten as follows,

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 5θ

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: The derivative of y=eSinh/x +cosh¬/x equals

A:

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: Find the nth derivative of the function y=xlnx at x=1.

A:

Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

A:

Q: Find the derivative of the function y, below. y = 2x(ln x + In 7) – 2x + V2 dy da

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

Q: 2) Find the first derivative of y = sec1(2e3*)

A: To find the first derivative of the given function.

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

A:

Q: 11) Find the first derivative of y = (ln x)*

A: We have to find the first derivative of given function.

Q: find the derivative of y with respect to the givenindependent variable. y = log3 (1 + θ ln 3)

A:

Q: y=

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.