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Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: The solution for the above question is as shown below.

Q: 8z 4. Assuming that z is a differentiable function of x and y, use implicit differentiation to find…

A:

Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

A:

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: 2) Find the derivative of f(x) = tan(1+ cos 3 x) %3D

A: As the function involved function in a function we can apply chain rule and find the derivative of…

Q: 4. Find by implicit differentiation of x sin(y) = y cos (x) dx

A: The given problem is solved below in detail.

Q: 3. (D - 3D? + 4)y = 40cos2x + 6

A:

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: Activity 2 Find the first derivative of the following: 1. y = ln (12x) 2. y = sin-¹ (x² + 3) 3. y…

A:

Q: 14) The derivative of y = cscx sin x is y = 0 A) True B) False

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: If f(x) is odd function, then the derivative of y =sinh (-x)) equals Select one: f'(x) O y'=- V…

A:

Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

A:

Q: 4.) f (x) 3D х2 – 1

A:

Q: MY The derivative with respect to x of the function y=-3tan-¹x-(In 3) log, (csc x) is y' = cotx + O…

A:

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: Can you help me step by step with this problem?

A: Given,

Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: find derivative 1. y = 1/( ln 3x)      2. y = ln (t3/2) + sqrt(t)    3. y = ln (sin x)      4. y =…

A: Hi! Your question contains many sub-parts. As per norms we will be solving only 3 sub-parts. Since…

Q: Compute the derivative of h(sin(x)) at x = assuming that h' (u)|=0,5 = 14. lu=0. Use symbolic…

A: Given:   Function : h(sin(x))    x = π/6 h'(u)| x = 0.5  = 14

Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

A:

Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

A:

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

A:

Q: find derivative  1. y = ln (3ue^-u)    2. y = ln (2e-^t sin t)  3. y = e^sin t (ln t2 + 1)

A: find derivative

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: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

A: we are given the function is  f(x)=1+sin2x2cos3x

Q: Compute the derivative of h(sin(x)) at x = assuming that h' (u)lu-0,5 = 6. %3D (Use symbolic…

A:

Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: 10. Find the particular antiderivative of the derivative f'(x) = 3x-1 – x-2 where f(1) = 5.

A:

Q: 1) Find the 3rd derivative of y = sin(x) %3D

A: To find the 3rd derivative of y=sinxx. Solution: For finding third derivative, we need to find first…

Q: 3. Find the derivative D(x *arctan(x)) And the integral 6x dx 9+x

A:

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 dy dx b) EVALUATE THE DERIVATIVE FROM PART a AT THE…

A: Given: x4y3=-8

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: 2- Find the derivative of y with respect to the Exercises 1-3. = 6 sinh 1- 1 sinh (2x + 1) 2- In…

A: These are the hyperbolic function so use standard form of derivative of hyperbolic functions.

Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

A:

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

A:

Q: Compute the derivative of h(sin(x)) at x = * assuming that h' (u)lu=0,5 = 10. (Use symbolic notation…

A:

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

A:

Q: |sin x.cos x %3D 1+ 2.ln x

A:

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: 5. Find by implicit differentiation for x + y = xy. dx

A:

Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

A:

Q: Example2: Find the derivative of w=xy+z if x=cos t ,y=sin t &z=2t?

A:

Q: Can you help me with this problem step by step?

A: Given: