Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable. (If an answer does not exist, enter DNE.) 4x f(x) x2 relative maximum (х, у) relative minimum (x, y) =

Q: 1. Using the definition of derivative, find the derivative of the following functions: (a) y= xVx-2…

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Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: Given function is: fx=-3x

Q: Calc 3 Find the indicated partial derivative. f(x, t) = x5e-ct

A: we have to find out the indicated partial derivative . fx,t=x5e-ct

Q: Can i get help step by step?

A: Rearrange the given ODE to get dy in terms of dx.

Q: Question The derivative of the function y e(tanx-2 vx) 1s:

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Q: B. Compute the derivative function f using the definition of the derivative. Show your complete…

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Q: Find the derivative, but do not simplify your answer. y = (x2 + x + 8)Vx - 2/x + 3 y' Your answer…

A: The product rule of derivative can be defined as, ddxu·v=vdudx+udvdx where u and v are two…

Q: Q-2: Find the derivative at each critical point and determine the local extreme values.

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Q: Q1) Find the Derivative to the function and find local minimum and local maximum points y = 3x? - 3

A: y=3x2-3 We need to find the derivative of the function and to find the local minimum and local…

Q: he partial derivative. x² 8x y-6xy. Find f, (x.y). 3

A: f(x, y) = x3 - 8x2y -6xy3 We have to find the partial derivative w.r.t y

Q: 1. Using the definition of derivative, find the derivative of the following functions: (a) y =xvx² –…

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Q: 5x Find the equation of the tangent line of the function eb-y at the point (2, 10). (y – 5) = 5(x –…

A: WE HAVE TO FIND THE EQUATION OF THE TANGENT LINE OF GIVEN FUNCTION AT (2,10)

Q: 3x-7 y: y%3D arctan 6. 6(x²+3) Find the derivative of the function

A: Given, y=tan-1x6+3x-76x2+3 Differentiating both the sides, we get…

Q: (1) Using the definition of derivative, find the derivative of the following functions: (a) y = xVx2…

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Q: Q3: i) Find the derivative of the function of y = (x² + 1)sin 3x %3D (ii) Find the absolute maximum…

A: Given:  i) y = x2 + 1sin3x ii) f(x) = x2-13, -3≤x≤3

Q: find the first derivative of x=1/t3 ; y=3t+t3

A: solution x=1t3 and y =3t+t3Now diff with respect to tdxdt=-3t-4 --(1)and dydt=3+3t2 --(2)Now, divide…

Q: Find derivative of the i function y = x*

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Q: Find the equation of the tangent line at the point

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Q: I am very confused on these two problems and I have homework due in 30 minutes.

A: Both problems concern finding deriviatives of functions ,using standard rules of differentiation

Q: xe* (a) Use centered difference approximations to estimate the first and second derivatives of y √x²…

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Q: Find the derivative of the function. y = 9 tan-(x - V1+ x² ) ,2 y' =

A: The solution of the problem is given in the next step.

Q: g(x) = e v find the derivative g'(x). 1 2e* 1 cev 2Vx e. B. A.

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Q: (x)=(2x +3) ² at x = 0. Find the second derivative of the function

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Q: The derivative of f(x) = %3D 3. 5' attains its maximum value at r =

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Q: c) Use Leibnitz's Theorem to calculate the 4th derivative of y = x^sin (3x) d) Locate and identify…

A: We have to solve part c and d.

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: 4ニ-3x*+2x ty Find derivative of yzfu) only using 4 definition of derivative

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: f(x)= 4/x , x=3. Use definition of derivative as x approaches 0

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Q: 6 Find the derivative of f (y) =7tan(y) - 6.

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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: 3.3 Find the derivative. y = 3x°e* %3D y' = II

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Find the derivative of y with respect to x. (x-y)^2=2ax

A: The given function is: (x-y)2=2ax To find the derivative of y w.r.t. x.

Q: 16. y= 3 cot(n6)

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Q: Find the derivatives of the functions y = (1 + x2) etan-1 x

A: Product rule (uv)'=u'v+uv' ddxxn=n xn-1ddxex=exddxtan-1x=11+x2

Q: a) Using the definition of derivative, calculate the derivative of the function of f(x) = /3x +1 (b)…

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Q: Find the derivative of the function. y = 13 arctan V (v²) y' =

A: We have to find the derivative of the function  y = 13 arctanx.

Q: find the derivative using the appropriate rule or combination of rules.

A: Consider the given function

Q: 1. Using the definition of derivative, find the derivative of the following functions: (a) y = xvx²…

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Q: 5x f(X) = V2x+3 %3D Find the first derivative given that

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Q: Apply derivatives to determine the critical points of the function ?=?(x−6)².

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Q: f(x)= 16x2-4x+2; x=1 (a) Find the derivative, by using the definition (b) Find the instantaneous…

A: (A) Found the derivative using the definition. Answer: f'(x)=32x-4

Q: Q2: Consider the implicit equation: y² – y – x² = 0 Find the implicit derivative dy/dx, and…

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Q: a) Find dx using implicit differentiation: x + y² = 2xy³ + 1 b) Find the equation of the tangent…

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Q: Find the derivative of y with respect to x Y=(7x+3)^x

A: Find the derivative of y with respect to x Y=(7x+3)^x

Q: h(x)=83x3+32x2+120x+9 Given the function above, use the First Derivative Test to find the local…

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Q: fidn the first derivative of y with respect to x using increment method y=2x^2-5x+7

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Q: e2x 2. Find the derivative of y = - (x² + 1)°(1 (1+ sin x)5

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