☺ using the definition f'sx) = li fCxth)-fx) find f'(x) when fex) %3D 2x-3

Q: What is the third derivative of 大 f(x): f(r) = 2 + cosx?

A: The given function is fx=x3+cos x. Evaluate the first derivative of the given function as follows.…

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx point (1,-1,1) in the direction 3i+4k x at…

A:

Q: Find the derivatives of the functions in Exercis

A: We have, f(x)=7+x sec x First, we write the above function in power form. fx=7+x sec x1/2

Q: ind y' by implicit differentiation: xy3 - sqrt (x2 +1)=2y

A: Definition used -    Implicit differentiation-  If equations do not define explicitly y as a…

Q: By using first principle of differentiation find f'(y), if ƒ(y) = Му—N

A: Given: f(y)= My-N According to the first principle of differentiation, the derivative of a function…

Q: Use implicit differentiation to find y' at (2, 0) for 2x2 + e2ay

A:

Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx %3D b. du = * c. du =-…

A: dx9-4x2=dx32-2x2 Put, u=2x⇒dudx=21⇒du=2 dx

Q: Find f'(x) using the delta definition of the derivative (i.e., limit process) vhere f(x)= x² – 5x…

A: Given that        f(x) = x2 - 5x + 12 Here we have to find f'(x) by using the delta definition of…

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: df Use derivative rules to compute where f(x) = -2xe". dx x%3DIn 7

A:

Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Find the derivative of the follourng funchion y=x sin'x %3D

A: We have to find the derivative of the given function   The given function is y=x sin-1x3it can…

Q: Find the derivative of F(x) = 4 sin(t) dt. 3x2 dx Jcos(x)

A: Given that,

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

A:

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

A:

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

A:

Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

A:

Q: Find the derivative of the function f. f(x) = e¯X tan(4x) %3D f'(x) = %3D

A:

Q: What is the relative error in estimating the first derivative of f (z) = 25x - 6x2 + 7x- 88 at x-2,…

A: Given equation is f(x) = 25x3 - 6x2 + 7x - 88∴ f′(x) = 75x2 - 12x + 7

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

A: y=12∫0xft x-t2 dt

Q: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

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

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

Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

A:

Q: Q1. By using the “definition of the derivative" find of y = v2x? %3D dx

A: Explanation and solutions is given below....

Q: Let f(x,y) = x³y? The third derivative fexy

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

A:

Q: 2x f(x) sec(t*) dt. %3D -2x

A: Given,            f(x) =∫-2x2xsect4 dt

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate 9.2 . %3D

A: topic - tangent line approximation note :as per bartleby guidelines we are supposed to answer only…

Q: Calculate the derivative of the function below using the quotient rule. 28 y = Vx + 8x7 f(æ) = %3D…

A:

Q: 3. Express the derivative of f (x) = Vx as a limit of the difference quotient ("h → 0")

A:

Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

A:

Q: HW prove That The derivative of Flx)=x-x is if (x) = 3x?1 use definition of devivativeto finid The…

A: Use following mentioned rules to find the derivative of the function. The power rule of…

Q: What is the relative error in estimating the fırst derivative of f (x) difference approach with…

A: We can solve this by using central difference formula and relative error formula

Q: Use the rule for reciprocals (수) - - to find the derivative: d 1 %3D dx lx2 Зх + 2

A: Given the rule of reciprocals as 1f'=-f'f2. It is required to find the derivative of 1x2-3x+2. Note…

Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

A:

Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

Q: 8. y = va? + x²

A:

Q: u=ex3 +y2z, where x=p ; y=eq ; z=sin r ; find ??/?? , ??/?? and ??/?

A:

Q: The directional derivative of f(x, y) at the point (a, b) in the positive y- direction is f (a, b).…

A: Solution: We know that if f(x,y) is a function of two variables x and y, then fx at a point (a,b)…

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

A:

Q: what is the derivative of hcx) at x =D0 where h lx) =2f(6)-2-VFIR) where %3D

A:

Q: dy Find dx if y = V5- x2 , by using definition .)باستخدام صيغة تعريف المشتقة( formula of derivative

A:

Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Use Dnf (x) to approximate the derivative of f(x) = sin(x) at ;h = (0.01,0.2) 4

A: Given fx=sinx at π4, h=0.01,0.2

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

A:

Q: Differentiate by using implicit differentiation x2y+xy2=6

A:

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

A:

Q: What is the derivative of f(z) = (z³ –- (z – 1)º)*? %3D

A: Given function is f(x) = (x3 - (x-1)3)3

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

A: