Consider the function f(x) = 12x' + 60x 100x + 6. f(z) has inflection points at (reading from left to right) x = D, E, and F

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 1. y Arctan- 3-V9-x2 2. y= 4 Arccos +…

A: 1.   From the given problem:   y=Arctanx3-9-x2   As we know:   d2ydx2=ddxdydx   So,…

Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

A:

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

A:

Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: Determine the differential of the function y=x3−3x2+4x at the point x0=1 when dx=0,1.

A:

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORN 3x-4 1. y = Arctan 2. y = 2 Arccos (1…

A: y=Arctan3x-44

Q: Let f(x, y) = sin(3x + 5y) and P = 3 Find the maximum rate of change of the fucntion f at the point…

A: Find gradient of f(x,y). Find compute the point . Take the magnitude of the same .

Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

A:

Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

A:

Q: Find the derivative of y with respect to x. y = (x° In x) ³ dy dx II

A:

Q: Use partial differentiation to find the derivative of the implicit function dy (3x'y-1)+ 7xy = 9…

A: We will use the given formula to solve this question.

Q: find the partial derivative of the function with respectto each variable. ƒ(x, y) = 1/2 ln (x2 + y2)…

A: The given function is fx,y=12lnx2+y2+tan-1yx.

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

A:

Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

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

A: To determine the derivative of given function.

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use…

Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

A:

Q: Find the derivative of F(x) = 4 sin(t) dt. 3x %3D dx cos(x)

A: Solve the following

Q: Find the partial derivative dz for the function z = cos(x³ +y²).

A:

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

A:

Q: Find the derivative of the function. f(x) %3D еx sec(9x) cos (9x) · e* + 7e* · sin(9x) f'(x) C cos…

A:

Q: Find the differential of the function y=xxe2x at the point x=1.

A:

Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: What is the value of the first order derivative of the closed function given as…

A:

Q: Find the derivative of the function at Po in the direction of u. 3x f(x, y) = tan -1 , P0(-2, 3), u…

A:

Q: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

A:

Q: Find the derivative. X dt 14) dx lol 0 5t+ 6

A: To find the derivative of given integral.

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: 22. Find the derivative of y = arcos(4x) with respect to x. - 4 4 - 4 - 4 В. 1-4x2 С. Vi-(4x) A. D.…

A:

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

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

A: Differentiate both sides w.r.t. x.And for addition we can apply the derivative separately on both…

Q: If z = (x + y) ev and x = 5t and y = 1 – t², find the following derivative using the chain rule.…

A: We are given that z=(x+y)ey,  x=5t, and y=1-t2. Now, we need to find dzdt.

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: Find the derivative of F(x)

A: To Determine: find the derivative of F(x) Given: we have Fx=∫2x3costdt Explanation: we have a…

Q: Find the derivative of F(x) = n sin(t) dt. 3x2 d dx cos(x)

A:

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: Find the derivative of y with respect to x. 6 y = (x³ In x) %3D dy dx II

A: Please see the below picture for detailed solution.

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 ; d'y/dx 1. y = 2. Y = (7x + 2)5…

A:

Q: Find the derivative of y with respect to x. 1 y = In x/x+5 dy dx II

A:

Q: 3r %3D 5r + 2 – 1 (d) f(x) =

A:

Q: Find the derivative of the function. 1 g(x) = dt Jtan(x) V2 +

A:

Q: b) Use implicit differentiation to find dy/dx of y² : X-1 x+1

A: Using implicit differentiation &amp; quotient rule.

Q: Find the derivative of y with respect to x if y = (10x- 20x + 20) ex. %3D dy dx

A: We can make it easier for you

Q: 1. F(x) = S, t³ - 5t dt

A:

Q: Compute the second derivative of e^x+y+y^2+x^3=0. y" denotes, d^2y/dx^2

A:

Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

A:

Q: Calculate the increment and differential of the function y=x2−x+1 at the point x=2 when dx=1.

A: Given, the function is y = x2 -x +1 at the point x = 2 and dx = 1, We have to calculate the…

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.