Let F(x) be an antiderivative of f(x), with F(1) = 20 and * f (x)dx = -7. What is F(4)?

Q: If (x, y) moves from (x0, y0) to a point (x0 + dx, y0 + dy) nearby, how can you estimate the…

A: The resulting change in function f (x, y) is given as:

Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

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

A: Differentiate both sides with respect to x. For xy use product rule

Q: Find the differential dy. y = 6x7 + 3x2

A: Given:y=6x7+3x2

Q: y =x3 dy Itx² -

A: Note  You type wrong Question here in place of dx/dy must be dy/dx  I solve it using dy/dx otherwise…

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: Find - by implicit differentiation. dx = y² + 2 x + y dy dx

A: differentiate wrt x

Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

A:

Q: Find the most general antiderivative. dx x2

A:

Q: What is the integrating factor y x² = 2 (2x - y)?

A: The given equation is; y'=2(2x-y).

Q: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

A: According to the given information it is required to calculate the antiderivative of the function:

Q: Find the most general antiderivative of the function. f(x) = + 3 cos x

A:

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

A:

Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

A:

Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: The general antiderivative determined by - x² - 3x +2 is dx

A:

Q: 3. f(x,y) tanx - sec²x - cosy

A:

Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

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

A: Given function is, x2+xy-y2=4.   It is implicit differentiated as follows:…

Q: determine dy/dx of the implicit function: 2x2y-sinxy2+e-xy=10

A: Given implicit function is  2x2y-sinxy2+e-xy=10 To find: dydx

Q: R(x) = F/2 π dx

A: We have to evaluate the integral: R→x=∫0π/2sin2x3x+1, lnx2-1,xx2+1dx   .....(1)

Q: Find dy/yx by implicit differentiation x^3-xy^2+y^2=2

A: Given function is x^3- xy^2 +y^2 = 2.Implicit differentiation is a special case of the chain rule…

Q: ( 2x2 , xs1 Dose f(x) = continuous at x =1?why? %3D &+ 1 , x >1

A: Explanation of the solution is given below....

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: Find the antiderivative of f(x)=cos(3x)

A:

Q: Find the most general antiderivative of the function. Check your answer by differentiation. 1 (8) –…

A:

Q: The integrating factor of Y + 3y cscx= cotx is?

A: Consider the given differential equation, y'+3ycscx=cotx This is the first order linear differential…

Q: Find dy/dx by implicity differation.

A:

Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

A:

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

A:

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: Find F'(x). *sin(x) 8Vt dt F(x) = F'(x) =

A:

Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

A:

Q: Find the general anti-derivatives. (a) Evaluate ∫ xsin x dx

A: We use integration by parts

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

A:

Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: Find dy/dx by implicit differentiation. 2) x3 - 2y2 = 1 4y B) x2 + 1 A) 4y C) 2y D) x2

A: solve the following

Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

A:

Q: Determine the most general antiderivative:  f(x) = sec x tan x-2e^x

A:

Q: Find a function whose 2nd antiderivative is f(x) = tan(x) + 4x+1

A:

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

A:

Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

A:

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

A:

Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

A:

Q: (B): Find the integration by using substitution method √x√2x-1 dx

A:

Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

A:

Q: If f'(x) = x*, what is f(x)? (Use C for the constant of integration.) %3D f(x) = %3D

A: