Given that f(x) = 2x + cos(x) is one-to-one, use the formula 1 (f-1)'(x) = f'(f-1(x)) to find (f-')'(1). (f-1)'(1) =

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

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Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: The derivative of In (cos x) is

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Q: What is the first derivative of g(x) = In 4x²+4x+8 ? x 3 tan x

A: we use Logarithmic properties

Q: 2х- 3 3. У3 5x +1

A:

Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

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: 4. Find the 2nd derivative of f(x)=14-x (x)%3D

A: The give function is fx=4-x

Q: The 2nd derivative of the given functions is 3 ponts y = 3 cos (4x- 5) None of the above -48 cos…

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Q: 2sin x -1 2. y = cosx+ 2

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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

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Q: 11 In(x)sin (x²). Find the first derivative of g(x) (x),6

A: As we know that: The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x The Power law:…

Q: Find the derivative of cos(3x) O -3sin(3x) O 3sin(3x) O 3cos(3x) O -3cos(3x)

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Q: FInd the derivatives of the function f(x) from the first pribnciple  cos2x

A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

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Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: find th first derivative: x=2cos2 t/2

A: we need to find the first derivative of

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

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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. -…

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Q: 1+ cos x y = In 1-cos x

A: This question is based on chain rule differentiation.

Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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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: g(x) = cos ¹x+ 1-x

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Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: what is the first derivative of cosx^2(x^2+2)

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Q: ,2, (x²–1)* Dx (1+8x)5

A: To Determine: find the derivative using chain rule  Given: we have y=x2-141+8x5 Explanation: we have…

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

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Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Find the derivative of ƒ (x) = cos-1(In(4x²+1)).

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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: Find the derivative of g(x) = e-" cos(x²)

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Q: How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because…

A: Given:

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

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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: Use the chain rule to find the derivative of: cos(7 + 8x)

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

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Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

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Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

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

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

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Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)