I. Find the derivative of the following functions using the limit definition. Show your solutions. ( 1. y=(3x-1) 3 2. v= 5-u 3. y=Vx

Q: Find the directional derivative of the following function at P(1, 0) in the direction that produces…

A: Given  fx,y = -3x2+4y3+2xe32y

Q: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

A: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

Q: If z = (x +y) eª and ¤ 3t and y = 1 – ť², find the following derivative using the chain rule. Enter…

A: See the attachment

Q: Find derivatives of the functions defined as follows: y = 73x+1

A: y=73x+1ory=73x·7ory=7·73x Use formula of derivative ddxax=axln a

Q: Find the approximate value of derivative f(0) with the step size h for the following function by…

A: The three point end point formula with error is where h is the step size. If the step size is…

Q: Find the derivative of function defined as follows.

A: Given: fx=82x2+5 Differentiating the given function fx with respect to x, f'x=ddx82x2+5…

Q: Compute the derivatives of the following functions. 4 y = Vx + cot(x5) x²e2x3 f (x) In(x4+2)

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Q: Find the derivative of the function using the limit definition of the derivative. f(t) = 2.5t2 + 6t

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Q: Find the derivative of the function by the limit process. g(t) = t3 + 4t

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Find the derivative of function defined as follows. p(z) = z(6z + 1)4/3

A: Given function is pz=z6z+143. To find the derivative of the function. Solution: Power rule of…

Q: Find the derivative using the definition. a. f(t) 2t+1 b. g(x) = 2x² +1

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Q: Use the "First Principles/Limit" to find the derivative of the function S(t) = t2 – t, at t = -1/2

A: Given  S(t)=t2-t To find the derivative using first principle at t=1/2

Q: Find the derivative of the function by the limit process. g(t) = t^3 + 5t

A: Using definition of derivatives,

Q: + (z), V1– 2z y =1- cos (z) + /1 – 2z

A: Given : y = xcos-1x+1-2x

Q: ) Given the following derivative function 2x – 5 f'(r) = Þ – I^ what are the critical numbers of…

A:

Q: Given the function z=(x2+1)(x−1). Find the value of its derivative at x=−1.

A: The given function is z=x2+1x-1

Q: Find derivatives of the function defined as follows.

A: Consider the given function as y=ex+e-xx

Q: Find the derivative of function defined as follows.

A: Derivative of the function can be found with the help of differentiation of the function.…

Q: Find derivatives of the functions defined as follows: y = (x + 3)2e4x

A: Chain Rule of differentiation: ddxf(g(x))=f'(g(x))g'(x) Product Rule of differentiation:…

Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The given function is: y=ln2x-1x+3 To find the derivative of this function, apply the quotient rule,…

Q: Find the derivative of the following functions by applying "Delta Method". Show your complete…

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: dy 4. Given y=5-4x find dx Ix-2

A: Given function is y=√(5-4x)  We find derivative of this function

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists .

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Q: Find the value of the derivative (If it exists) at the Indicated extremum. (If an answer does not…

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A: Explanation: The given function is: f(x)=-3xx+1 Find the first derivative of this function.…

Q: Given the function y=(2x+1)3(x−1). Find all derivatives of the nth order from n=1 to n=5.

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: Obtain the derivatives of the following functions f(æ), using the Simple chain rule and enter your…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the derivative of the followi (a) x = t2 + 5t + 4, y = 4t

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Q: Find the derivative of y with respect to x in the following functions: y= Ju +2u and u x2-3

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Q: Find the derivative of the following functions using the long method (limits) (a) x = t* – 5t – 3…

A: (a) Consider the equation x=f(t)=12t4-5t-3 To find the derivative of this using the limits.  So we…

Q: Find the derivative of y with respect to x in the following function at (1, 1/3) u? y = u' +1 and u…

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Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: (0) x %3D 글*- St-3 5t – 3 2

A: Explanation of the answer is as follows

Q: Find derivatives of the functions defined as follows:

A: Given that : The function is y = tet + 2e2t +1 .

Q: Given that f(x) = (x-2)/(x+3), find the slope of the tangent line at x = 2. %3D O a. 1/2 O b. -1/5 O…

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Q: a. Compute the derivatives of the following function: sec(xy) = 4x(3x+ 5)5 b. Find an equation for…

A: Product Rule of differentiation : d(u.v)dx=u.dvdx +dudx.v dxndx = nxn-1 Equation of line passing…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = x2…

A: Solution:-  The given function is  g(x)=x2-xwe have to use alternative form of derivative to find…

Q: I. Find the derivative of y with respect to x. Use the given relation in its implicit form. d?u 3.…

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Q: 6. v(y) = In (y² – 8y – 1)

A:

Q: Find the derivative of the function at P, in the direction of A. 2 f(x.y) = 4xy- 4y, Po(6,8), A= –…

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Q: 3) Use the definition to find the derivative of f(t) = +1 t+1 %3D

A: f'(t) = -1/t2

Q: Find derivatives of the functions defined as follows: . y = 1.2e5x

A: the given function is: y=1.2e5x we have to find the derivative of the given function.

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A:

Q: Find the derivative of the function by the limit process. h(s) = −2√s

A: h(s) = −2√s

Q: Find derivatives of the functions defined as follows:

A: Our Aim is to find the derivative of the function given below:-y=t2 e2ttt+e3t-(i)

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) =…

A: The alternate form refers here the definition of derivative.