B) Find the derivatives of the following functions: (for only 6) 5) y- In ( sin' 0) 6) y = log:() 7) y-t tanh 8) y = xe" - e

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: 10. Find the 87th derivative of y = cos(2x) at IT

A:

Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

A:

Q: 6. Find dy/dx by implicit differentiation for tan-'(²y) = sin(x²) + 3ry?.

A:

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

Q: 1. Find the first derivative " if y = x sin 27x . dx

A: Given:  y=x sin 2πxTo determine the firstderivative.

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORN 3x-4 1. y = Arctan 2. y = 2 Arccos (1…

A: y=Arctan3x-44

Q: Find the differential equation characterizing the family of curves described tangents to ky = x^2

A: We need to find the differential equation characterizing the family of curves described tangents to…

Q: What is the derivative of x sin(x) at the point (6,5)? 2 O 1 O-1 O None of the above

A:

Q: Find the derivative of y=cos4 x sin4 x Ans: 1/2 sin3 (2x) cos cos (2x) solution?

A: We simplify the given expression using the double angle property

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

A:

Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: #11, find dy/dx by implicit differentiation

A: Differentiate question 11

Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

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

Q: By climinating the arbitrary constants, form the differential equation in the fotowng cases: 1- y2 A…

A:

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

A: The given equation,

Q: y = e* (In x)² %3D

A: Here we want to find the first derivative of the given function. For finding the derivative we use…

Q: If the graph of f(x) has a parent graph of y = sinx and a phase shift of 6. maximum value to the…

A: Given: y=sinx

Q: Find the derivative of the function. Y= q56* In(2)ln(5)ln(6)· 3*. 5".; 2:56*+1+x

A: Given problem:-

Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

A:

Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

A:

Q: Find the differential equation of family of circles tangent to the x-axis.

A:

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: S Sin 5t-205 2t-2(03 2€ ; s(登)=

A:

Q: In (1 + 2), What is the derivative of y .? e2z %3D

A:

Q: In (6x) Find the derivative of y with respect to x if y = sin (3e) dt.

A: the given function is: y=∫0ln(6x)sin3et dt we have to find the derivative of y with respect to x.…

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: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

A:

Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

A:

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

A:

Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

A:

Q: Find the first derivative of the following: 1. y= y = Ine-tanh² 2x 2. Y= sech(5x-1)tanh(5x-1) 3.…

A:

Q: find the first & second derivative of fox)=e 2. Cosx.

A: Given: The function fx=x2excosx, To find: First and second derivative of given function fx.

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: x3+6x-2 dx x4+6x2

A:

Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

A:

Q: 5. Find the derivative of --( 1 + sin 0 cos 0

A:

Q: 3. If the derivatives of h with respect to U; for h=²u

A:

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

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

Q: Y = 2 Arccos ( 1 -) + v4x – x²

A:

Q: 1. Find by implicit differentiation for xe = 2xy + y³.

A:

Q: 4. If y = x cos x determine the 5th derivative. [y6) = (60x – x³) sin x+ (15x? – 60) cos x] |

A:

Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows