Compute the derivative function f'(x) algebraically. f (x) = 3x2 +x lima 0 (6z + 3h + 1) = 1 limp 0 (6z + 3h + 1) = 6z + 3 limp 0 (6x + 3h + 1) = 6x + 1 lim (G 91

Q: 3. Given the equation y = x³ - 3x² + 3, determine all Critical Points and classify using the SECOND…

A:

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x² – 1)³(x² + 3)² x3+4x…

A: Given functions to be differentiate are    1.   y=x2-2x3+4x    3.  y=x2-2x      we will make use…

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: Find the derivative of the function by the limit process. f(x)= 2/x2

A:

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

A:

Q: Find the derivative of f(z) = e2" (3z2- z)

A: Given, f(x)=e2x(3x2-x) Here, when we try to find the derivative of f(x), both chain rule and…

Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Calculate the partial derivative using implicit differentiation of ey + sin (9xz) + 4y = 0. (Use…

A: Use the following: 1.(ef(y))'=ef(y)f'(y)2.∂y∂y=13.(sin f(y))'=cos f(y)f'(y)

Q: 1-x Find the derivative of y = arctan %3D 1+x

A:

Q: Find the local maximum, minimum and saddle points of the function using the second derivative test:…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 (1/2)θ

A:

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: Compute the derivative using derivative rules.

A: Explanation Given that,  y=(kx+b)-13   Differentiate with respect to x both the sides…

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt 1 2 arctan(2x) F'(x) = (arctan(Vx)) -

A: Here we have,

Q: What is the derivative of f(x)=3cos(x)+2sin(x) at the point x=−π

A:

Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

A:

Q: COs X Compute the mixed second order partial derivative of z =

A: The mixed second order partial derivatie of z=cos x y5  is given by ∂2z∂x∂y=5sin xy6

Q: Find the slope of the curve y2 + x² = y* – 2x at (-2,1) Find the required derivative by applying the…

A: topic - slope of curve note - As per bartleby guidelines ,we are supposed to answer only first…

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

A:

Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

A:

Q: Compute the derivative using derivative rules.

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: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: 3) Find the derivative of the function f(x)= x² –x+2 using the definition of the derivative (a…

A: Given:     To determine: Derivative of the function using the definition of the derivative.

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: Derivative of y with respect to x

A: taking logrithum both sides and solve the question.

Q: Find the derivative of the function by the limit process. f(x) = 3x- 1 - (x), J

A: fx=3x-1

Q: Find the derivative of y: 1- y = (cos 0)V2 Cos O 2- y = 7sec ln 7 3- y = 2sin 3t

A:

Q: Find the derivative of the function by the limit process. f(x) = vX +7

A: Given,          The function is fx=x+7.

Q: Find the derivative of the function using chain rule. f(x) = esin?x

A:

Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

A:

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: What

A: The correct option is (B).

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: 04:- Use the Chain rule to find the derivative ) of z = 3x2 - 2 xy y and If x=x (u, v) = 3u + 2v and…

A: Please refer to the image below.

Q: How do you find the partial derivative of a given function using the definition formula?

A:

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

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

A:

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

A:

Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

A:

Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

A:

Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

A:

Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

A:

Q: r(x)= cos (3x)

A: