Given that f"(x) = cos(x), f'(T/2) 2 and f(T/2) = 11, find: f'(x) = f(x) =

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

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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: Find the derivative of y with respect to x. y = In (tan 1(5x)) dy dx

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Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: Find the 80th derivative of y = cos(2x).

A: The given function is y=cos(2x)

Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

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Q: 3. Find the derivative of the function. y = In(t2) – arctan(-

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

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Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: Find the differential d8y of the function y=exsinx.

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Q: A// Find the derivative of y with respect to x 5) 3tan-1x + sin-1x = 4 6) y = ln- 1+ ex = la,

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Q: Consider the function f(x) whose second derivative is f′′(x) = 18x + 3 cos x. If f(0) = 4 and f′(0)…

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Q: Find the differential equaiton corresponding th y= a cos(log x) +b sin(log x) where a and b are…

A: Differential equation formation

Q: Find the derivative of the function. sin(x) y = In(1 + 6v) dv cos(x)

A: Find the derivative of the following function

Q: Compute the higher derivative.

A: Given, d3dx3sin 2x

Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

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Q: 3. Find the derivative y'(x) implicitly. cos²x + cos²y = = cos (2x +2y)

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Q: The derivative of: y =0( sin (In (0))) in (In (0))) + cos(ln (0)) is is:

A: Given function is rewriting in other variables as: y=x(sin(ln(x)))+cos(ln(x)) Product rule of…

Q: Find the derivative of the function. f(x) %3D еx sec(9x) cos (9x) · e* + 7e* · sin(9x) f'(x) C cos…

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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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

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Q: Find the differential of the function y=xxe2x at the point x=1.

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

A: This question is based on chain rule differentiation.

Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

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: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: Find the derivative of the function sin(x) In(6+4v) dv cos(x) y y'(x)=

A: The given function is,

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 y' by implicit differentiation: 8 cos(ry) + x4 = yª

A: Given: 8cosxy+x4=y4 For finding derivative of given expression, we differentiate given expression…

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 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: Find the first derivatives of y = cos x tanx

A: Given: y=4cos x+1tan x

Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: If the first derivative of y is -3.8025 sin(0.507 t) on the interval {0 <= t <= 24}, what are the…

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

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

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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 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: c. Find the derivative of y =+- et x3 cOS X 2

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Q: The derivative of: y =0(sin (In (0)))+cos(In (0 )) is:

A: Given :y=θ(sin(ln θ))+ cos ln θ dydθ=θcos ln θθ+sin ln θ-sin  lnθ θ      =cos ln θ+sin ln θ-sin  lnθ…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

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Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

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