Given that f(x) = sin((7x + 6)4), find f'(x) as a function of z. f'(2) =

Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

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Q: In y = 22 cosh1 2x

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Q: Find the Equation of tangent line of the function f(x) = 1 + csc(x) – /cos(x) 2n 4+V3 23 At the…

A: Consider the provided function, fx=1+cscx-cosx and the given point 2π3,4+323. Find the equation of…

Q: Find the derivative using the long method y = vx + 2

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Q: compute the derivative y = sin(2x) cos2 x

A: Given y=sin(2x)cos2x The product rule of derivative is given by:

Q: 2х- 3 3. У3 5x +1

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Q: Find the derivative of y with respect to x 3tan-1x + sin-1x = 4

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Q: Which is the derivative of y= sin (x2-2x + 1)? (2х -2) (2x-2)Cos(x²-2x + 1)

A: We have to find derivative

Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

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Q: Find the derivative of f(x) = 2(x² + 3x) cos(sin(x³)).

A: I have used product re and derived of composition of two function

Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

Q: Find the first and second derivative of y = e^−2x(cos3x+sin3x)

A: The first derivative of the given function by using the product rule of the derivative:

Q: compute the derivative. y = sin(2x) cos2 x

A: We can find the derivative of this function by using the product rule of differentiation . According…

Q: Compute the higher derivative.

A: Given, d3dx3sin 2x

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: 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 derivative of the function. y = (( 1- cos 2x ) /( 1+ cos 2x ))4

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Q: In(x), Sn (4t + et) dt. Find the derivative of F(x). 3.

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Q: Find the derivative of the function f(x) = at sin(7x + 14) + In(2r+10)

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Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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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: 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: Find the derivative of the function In (2x+10) f (x) = x* sin (7x + 14) +

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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

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Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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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: Find the first And 2nd derivative  F(x)= e^x sin4x

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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 the function. "sin(x) In(7 + 9v) dv /cos(x) y'(x) =

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Q: The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)

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Q: Find the derivative of the function. sin(x) y = /cos(x) In(8 + 3v) dv y'(x) = 0

A: Here we use Leibniz integral rule and define the formula:

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

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+v3 3' 2v3 At the…

A: Given: f(x) = 1 + csc(x) -cos(x)   To determine: Equation  of the tangent line at the point…

Q: Which is the derivative of y= sin (x2-2x + 1)? О 2х-2) (2x-2)Cos(x²-2x + 1) O Option 2

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Q: Find the derivative of y with respect to x. y = 3 sin -1 (5x 3)

A: Given data:     The given expression is: y=3sin-1(5x3).   Assume 5x3=u and differentiate it with…

Q: Find the derivative of y with respect to x. y = 4x sin -1 (4x°) + /1– 16x' y = 4x° sin -1 (4x°) +…

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Q: How would you find the derivative of sin (z^6) + sin^6 (z) using the chain rule?

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Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: Find y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x   and  y = (e-x)/…

A: Solution -a.)Given function -y = 5x2+6x-7lnxDifferentiating on both sides with respext to x,dydx =…

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

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Q: What is the derivative of the: y = (1 + cos2 x sin x2)3/2

A: Given: y=1+cos2x sinx232 differentiate with respect to x, dydx=ddx1+cos2x sinx232dydx=321+cos2x…

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

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Q: Find the derivative of f (x) =arcoth (e³" ).

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Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…

A: Given:- y = (-7x2-5x+5) (sin(x) +11x)  To find:- Derivative of y

Q: y = sin(3x²) cos(3x²)

A: