For fx)= 1+ 1 +음 + we have: f'(x) =

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Find the derivative of f(x) = In(x² + 1) %3D

A:

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: FIND THE DERIVATIVE BY THE LIMIT PROČESS OFF(x) = Vx+2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q1 Prove that the derivative of (2x +1) 2 is 4 (2x + 1) by using first principle derivative.

A:

Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

A:

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A:

Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

A: The given function y=71-14x2

Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: f(t) = In- t

A: Given f(t)=ln(1/t) We need to find the derivative of the function.

Q: If g(x) = In(6x6 - 2), then the derivative of g'(x) is 676 36z5 1 6x5 626 36x5 1. 3675 1 6x6 O O

A: We will use simple differentiation rules to solve this question.

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: Compute the derivative of ln r3 –1 V2x+5x²

A:

Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

A:

Q: Compute the derivative of 6x2 f(x) = In(r) %3D

A: We have to find derivative

Q: Q1 Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A: as per our guidelines we are supposed to answer only the first question. Kindly repost other…

Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Find an anti-derivative F(x) of f(x) = 7x³ – 6x² –- 1 satisfying that 7 F(1) = 4

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) y…

A: We have to find derivative

Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

A:

Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: Find the first and second derivative if w = 3z-2-(1/z)

A:

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

A:

Q: Find the derivative of f(z) = (x³ + 5)(z³ – 5) %3D (8z")(5x*) (8z +5)(z – 5) + (z³ + 5)(5x* – 5) (8z…

A: We need to use the product rule.

Q: Find the derivative using the long method 3 u = t2

A:

Q: 3/ By using the definition of derivative, proof that tan x = sec? x. %3D dx

A: By definition of derivative , f'(x) = d(f(x)dx= limh→0f(x+h) - f(x)h L Hosital's Rule :When limit is…

Q: What is the second derivative of y = 6x² 3x³ + x² - 5 ? - Oy"= 72x² 18x + 2 Cinema) Oy" 24x³9x² + 2x…

A:

Q: find the derivative af: 5y 2.5x/2 1) =xe ye

A:

Q: Find the derivative by the limit process. f(x) = 11-x²

A:

Q: Find the derivative. Using Chain Rule y = (2x2 – 1)3(3x² + 1)³ |

A: According to question,Given Function,y = 2x2-133x2 + 13

Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3…

A: We have to find derivative of Given function.

Q: determine maximums and minimums by the Second Derivative Test, we differentiate y"=72 / (2-8)3…

A: topic  - local maxima and minima

Q: Find the derivative of f(x) = 4Vx + +4. O 4 + In(x) 4 x3 O 2 2 .2 O 2-4 O 2/x 4x-2 | 2

A: Given function is fx=4x+2x. We have to find the derivative of fx=4x+2x. Differentiate fx=4x+2x with…

Q: Find the derivative. (Hint: do chain rule. ) * 12° dt 6x 8x6 12x/2

A:

Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

A:

Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

A:

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. x. g(>…

A: We know that, the First Fundamental Theorem of Calculus says that if f be a continuous real-valued…

Q: Obtain the derivative of the function y (ctg(5x))} y =- - sen? (5x) + 1

A:

Q: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

Q: Find the derivative of f(x) = In2x 2 2z

A: We first use the addition property of logarithm.

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Find the first derivative: y = In V2x3 -5 222 O y' = 2z3-5 5z2 O y' = 223-5 3z2 O y'= %3D 223-5 O y'…

A: Using Chain rule Y= f(g(x))  so Y' = f'(g(x))•g'(x)

Q: Find the derivative of f(z)=((11z+4)1/2)(e3z).

A: Given function f(z)=11z+412e3z

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: