If S(x) = - cos(x), then s ()(x) is equal to A – sin(x) - cos(x) В sin(x) cos(x)

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

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Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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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: , Suppose that the tangent line to the graph of f(x) = xlb) at r = 1 is equal to the tangent line to…

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Q: Find the derivative of f(x)=sin sin(5x

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Q: 17) Find the first derivative of f(x) = (cos4x)6 6 or f(x) = cos 4x

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Q: Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

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Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

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: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

A: cos2x=cosxcosx-sinxsinx find the derivative of cos2x So here use product rule and then find…

Q: Find the derivative and show your complete solution of the following 1. cos(e ^ (2x) + e ^ (- 2x))…

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Q: Find the 46th derivative of y = cos (x) sin (a) cos (2) cos (x) - - sin (x)

A: Given y=cosx

Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: sin x (cos x+1) dx 7. S (cosx +1)2

A: Given that: ∫sinx(cosx+1)(cosx+1)2dx           NOTE: As per our answering guidelines, we can only…

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: In this problem, please evaluate the trig functions without a calculator and de tion of the tangent…

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Q: I need to find the derivative of the function f(x) = cos-1(ln(sin(3x+1))) but I am unsure how to…

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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: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-x)

Q: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

A: Critical points are the points where the derivative of the function is zero or undefined. Our…

Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: Find the first derivative of y = cos4 x – sin4 x and y = x3   –  x2 cos x  +  2x sin x  + 2 cos x…

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

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

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Q: g(x) = cos ¹x+ 1-x

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Q: What is the derivative of y = 10sin 5x 5 In 10 cos x 10in 5x 5 In10 (10sin Sx) A. C. 5 cos x In 10…

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Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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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: What is the second derivative of y = 2x -+ sin x with respect to x? a. 2 -+ cos x b. 2 ++ cos x -+…

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Q: y=ln(sin(X3-1))

A: Detailed explanation is attached below.

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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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: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to

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Q: Find the first derivatives of y = cos x tanx

A: Given: y=4cos x+1tan x

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: 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 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: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: What is the derivative of y = 10sin Sx 5 In 10 cos x 10sin Sx 5 In10 (10sin Sx ) A. В. C. 5 cos x In…

A: Given: y=10sin 5x To Find: The derivative of the given function.

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

A: We have to find out derivative

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

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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: Compute f sin(cos(x²)) sin(x²)x dx

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