Find the actual error when the first derivative of f(x) the following 3-point formula sin(2x) at x = 1/8 is approximated by %3D %3D 3f (x +h)-2f(x)- f(x-h) f'(x) 4h with h = 0.25. O 0.5544 0.0431 0.0343 O 0.2313

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Q: Find the derivative of the function y = cot^-1 x^2– cos^-1 (x + 1/x – 2). %3D

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Q: Find the derivative of the following function. f(x)=ln(e2x+3) evaluated at X=ln 4 The value of…

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Q: 5cos3(x) Гу 3 sin(3–2x) + tan? (3x? — 4х) — csc(/2x — 1

A: Differentiate y w.r.t x.

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: 1) Find the derivative of the function g(x) = (arctan x)3, first showing how to get the d formula…

A: As per guideline we have solve only one question

Q: Q4 / Find the value of derivative below * If y = x/1 - x² + Cos-1(x) then y'at | x = is

A: Given,y=x1-x2+cos-1(x) dydx=dx1-x2+cos-1(x)dx=dx1-x2dx+d(cos-1(x))dx

Q: 4) fG) = (2x+ 1)9 %3D

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Q: Calculate the derivative of y with respect to x. Express derivative in terms of sin (y³) (Express…

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Q: 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = X-…

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Q: . h(x)= cot 1 -tanx

A: Given:hx=cot-11x-tan-1x

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: а. h(x) —…

A: We need to find derivative.

Q: Find (i) the first derivative of f(x) = 3 x³. Inx + 5 e*. sin-1x + tan-1(4x) (ii) the second…

A: To find the following parts,

Q: 4. Determine the following derivatives without simplifying either before or after. (YOU MAY USE ANY…

A: Using given formula then solve it.

Q: The derivative of the function y = x(tan-(3x))? is: Lan"as (1n)tan a the above the above tan"oa +…

A: This question is based on chain rule differentiation.

Q: (b) Find a general expression for dy - (x), the (implicit) derivative of y with respect to x, as a…

A: given rθ=2+2cos2θ   for θ∈[0,2π) (b) find a general expression for dydx let  x=rcosθy=rsinθ…

Q: What is the approximate value of the first derivative of the y = sinx function at x =pi/4 when you…

A: The first derivative of the function can be obtained using the forward and backward difference…

Q: x²+x' Evaluate the derivative at x = 1 for y = In () %3D

A: Some common derivatives are, ddx(ax)=ax.loga+C ddx(logf(x)=1f(x).f'(x)+C Quotient rule of…

Q: Q 7. Is cos x| differentiable in (-oo, oo). If so find its derivative. If not, is it differentiable…

A: Let us begin with plotting the graph for |cos x|.

Q: х+1 3.) y = х-2

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Q: The third derivative of y = sin is 1 -sin b) y" = --cos 1 а) у 8. 2 2 c) y" =-8sin d) y" = -8 cos

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Q: Find the equation of the line tangent to the graph of f(x) = (In x)? at x= 8.

A: f(x)= (lnx)2

Q: 1. a) Find the derivative of the function y = sinx + cosx. %3D b) What is the value of the…

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Q: How do I find the derivative of (Sin^-1(1/x))? What rules do I use?

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Q: 2 cos x 4. Consider the function f(x) = x2 find its derivative

A: Given function: fx=2cos xx2Differentiate the above function w.r.t 'x' f'x=ddx2cos xx2

Q: Q. 2. a) Find nth order derivative of f(x)= ln(2x-7). b) Find 3rd order derivative of y with respect…

A: The function fx=ln2x-7. The first derivative of the function fx=ln2x-7 is computed as follows,…

Q: nd the Derivative : f (x) = cos (x)° (sin°(x + 3x)) 3 = CoS (

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Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

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Q: 2. y = a Cos-1 (1 -2) + V2аx — х2 a

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Q: The third derivative of y = sin is b) y" =-co а) у -sin 8 c) y" = -8sin d) y" =-8cos

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Q: 3x dy of y = Find the derivative, dx x2 + 1 O 3(1 – x²) (1+x²)² O 3x2 – 3 (1 + x?)3 - O 6x+x² (x² +…

A: Given: y=3xx2+1

Q: Find the derivative of y with respect to the appropriate variable → 49. y = cos '(x²) sin-'V2! 50. y…

A: Solve the following marked questions

Q: Find the derivative of the function y=  Square Root of 2−7x and evaluate it at x=0.   Square root of…

A: Given function, y=2-7x To find, dydx at x=0 Formulas used, ddxxn=nxn-1ddxconstant=0ddxCfx=Cddxfx…

Q: 4 %3D ») f(E) =

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Q: 4 sin x-3 2. Find the first derivative of y =150xcos (10x)+ 9 In(J16-x)

A: use derivative of y

Q: 11. In y = e" sin x

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Q: 2the second derivative test to find the loscal maxilnum and minimulin of thie functioni 3 f (x}こ 2メ2…

A: To find the local maxima and local minima of the below function. fx=2x3−3x2−12x

Q: Find the indicated derivative. Find y(4) if y = -6 cos x. O y4) = -6 sin x O y(4) = 6 cos x O y4) =…

A: Given:  y = - 6 cos x

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

A: Taylor series

Q: 3 5.) y = ; x+5

A: Given:- y = 3/(x+5) y = 3(x+5)-1 Using Formula : [f(x)g(x)]' = f(x)g(x)' + g(x)f(x)' Now, y' =…

Q: Find the first derivative f'(x) the the function f(x) = cosx vt +5

A: To find the derivative of the below function

Q: Derivative OF the FollOwing 1.y sin x)* 2. y-Tex te* 3. d dx ( scextanx t in csccxttanx)

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Q: 5cos³ (x) Find the derivative of y + tan²(3x² – 4x) – csc(v2x – 1 )and express your sin(3–2x) answer…

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Q: |sin x.cos x %3D 1+ 2.ln x

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Q: Find the derivative of y=(e^2x)sin(5x)

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Q: Find the third derivative [f"(x)] of the given function: f(x) = 8 sin() %3D

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Q: What is the derivative of f(x)=−3cos(x)+4sin(x) at the point x=π/3? Enter an exact answer.

A: Given,  f(x)=−3cos(x)+4sin(x)   We have to find the derivative of fx  at  x = π3

Q: x² +2x+1 6.) f(x) = 3

A: The given function is f(x)=x2+2x+13. Find the first derivative or f'x of the functions by using the…

Q: 1.) f(x) = (2x + 1)(3x – 2)

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Q: Can i get help step by step please

A: We have to use the power rule because of exponent -1 and then use the chain rule for (cscx-cotx).