Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0). Assume also that f(3) = -12 \f(x)| < x* + 8 and f(x)e¬x/3 dx = 6 Determine the value of I s'(x)e³ dx

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Q: i. y= ) In (x+3

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Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

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

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Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

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

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 y with respect to x. y = sec -1 (3x2 + 1), X>0

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Q: Find the derivative of function.

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Q: Find the anti-derivative of g(x) = sec(x) tan(x) which contains the point (TT, 0). O G(x) = -csc(x)…

A: Solution to the anti-derivative can be found by integrating the function.

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

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

A: The given equation,

Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

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Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

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Q: Find the derivative of the function. 1- e3x 1 + e3x y = cos y' =

A: Given that: y = cos1-e3x1+e3x To find: We have to find the derivative of the given function.

Q: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x =; using a…

A: The three-point midpoint rule to calculate f'(x) is f'(x)≈f(x+h)-f(x-h)2h, where h is the step size.

Q: 2. Find the derivative of f(x). (a) f(x) = x² sec x (b) f(x) = 1+ tan a 1- tanz

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Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

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

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Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

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Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 (x2 + 1), x &gt; 0

A: Given that, y=csc-1x2+1

Q: (b) Use implicit differentiation by partial derivative to solve for dx of the function 5x + xy 4y.

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Q: Find the derivative of the function using implicit differentiation.  1.) x²y + y²x = -2  2.) √(xy)…

A: 1.) x²y + y²x = -2    2.) √(xy) = x²y+1 ntiderivatives for integral notation. (x+7) dx

Q: derivative of a Y with respect to x Y= ln (15x)+3x dy/dx=

A: Use formula of derivative to solve

Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

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Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

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Q: sinx (a) h(x) = tan(x² sin.x) (b) y= V1+cos.x

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Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

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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: 3. F(x) = " In(x) (4t + et) dt. Find the derivative of F(x).

A: Given, F(x)=∫1ln(x)(4t+et)dt To find : Derivative of F(x) By using the second fundamental theorem of…

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A: On simplification, we get

Q: (a) Show that the derivative solution of this function y = x** is x(x*+x-1) [1+x In x (In x + 1)] dx

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Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

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Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

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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 y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

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Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

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