Suppose 8 (x): c-(x²). what is the derivative of g with respect to x? = sec 2 A 8 (x)=- xV1-. B 8'(x) = x4– 1 2x © 8'(x) = Vī-x+ 1-x4 1 D 8'(x) = x²Vx+-1

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 2. y = 2 Arccos (1-x/2)+ Square root of…

A: Second order derivative.

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: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

A:

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: HiHtar is THe secoyd derivative OF Y

A:

Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: Determine the derivative of the following functions. 1. у 3 (8ӕ — 1) sinh(8a — 1) 2. y = (5)…

A:

Q: Find the derivative of f(x) = 1 at x = 3

A: The given function is: fx=1x Using the formula of derivative i.e., ddxxn=nxn-1

Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

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 first derivative of f(x) = ln 3z²+7z ?

A:

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

A:

Q: 2. In y = 2" + x cosh 2x

A:

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: Solve for the derivative of the function using chain rule. 11. f(x)= ln(sin(8x))

A:

Q: 8. Find the derivative of y = x arctan 2.x --In(1+4x). -- - 4.

A:

Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: find the equation of the tangent line to the graph of f(x) = x^3 + 3x^2 at the point (1, 4) without…

A:

Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

A:

Q: In 2x y = - cos x

A: ddxln 2xcos x= ddxln 2x . cos x - ln 2x.ddxcos xcos2 x= 12x. 2. cos x - ln 2x.(-sin x)cos2x= cos xx…

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

A:

Q: Find the derivative of f (x ) =V sech( In (8x + 1)) - sech(In(8x + 1)) tanh( In(8x + 1)) A 2/ sech(…

A:

Q: Which of the following has a derivative of f (x) = 2x (arctanx + arccotx)?

A:

Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

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

A:

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

A:

Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

A:

Q: Calculus 11th Edition - Ron Larson Please assist with the question below. Please show &…

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

A:

Q: Approximate the derivative of f(x)-x3+4x2-10x+5=0 at x=3 using the forward, backward and central…

A:

Q: Solve for the derivative of the function using chain rule. 7. f(x)= sin(e3x)

A:

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Solve for the derivative of the function using chain rule. 14. f(x)= 3lnx 15. f(x)= cos(cosx))

A:

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM х 1. y= Arctan- 3-V9-x²

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

A:

Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

A:

Q: Find the 2nd derivative of (y^2)+cosx 3y +1

A: This question is based on Derivative of equation.

Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: 1.Find the derivative of y = - arcsin %3D V4-x2

A: Given:        y=x4-x2-arcsinx2 differentiating on both sides     dydx=ddxx4-x2-arcsinx2…