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Q: 1. Find the derivative of each function below. ex² - 3x +1 y = In(2e¬t sin t) A y =

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Q: Consider the the following equation. x² y + xy = e Which of the following represents the derivative…

A: To find the derivative of the term

Q: (a) Find dy – Ay, if y = 6 – 7x (b) Find the derivative of f(x) = 2(cos4x - sin4x) Solution.

A: Solved below

Q: 1. Find the derivative of the following: 1² + 2r + 1 a) f(1) = r3 - 5x + 3 b) G(2) - VP+1 dt e) y…

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Q: Provide the equation of the line tangent to the given function at the specified point g(x)=ln(x^2);…

A: Given : gx = lnx2

Q: Find the derivative of y with respect to x. y = In 6x? 12 O A. 2x В. x + 6 Oc. OD. 2x +6

A: The given function is- y=ln6x2 Differentiating y w.r.t. x- dydx=16x2×d6x2dx

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

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Q: In the given question/s , find the derivative of the function.   y = ln l sin x l

A: Consider the function: y=lnsinx

Q: Given that the first derivative of x^81+y^81=-36 is given by dy/dx=kx^c/y^c,what is the value of k?

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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: Answer all of the following questions. 1.) Find the equation of the line tangent to f(x) = 6 ln(7–…

A: Answer and explanation is given below

Q: 1. Find and simplify the indicated derivative: (a) D: [e¯t sin(2t)]

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Q: Q2/ Find the derivative of each of the following functions:- X 2. log₂ x y = X 1+ tan x 1. y=(sin…

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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 the function. h'(t) = h(t) 2 sinh(−4t)

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Q: xy2 + x tan y = y sin b. ye* + sin xy = x tan xy a.

A: a)To determine the derivative of the function given by; xy2+xtan(y)=y sin(x)  Differentiate both…

Q: Solve for the derivative of the following function: v=1/t^3

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

A: f(x)=(x+5)23  f'(x)=23(x+5)-13  f'(x)=23 (x+5)3Let's understand f'(x) as a different…

Q: In the given question/s, find dy /dx by implicit differentiation :-   x2 + y2 = 9

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: te 2. 2t t.

A: Given,            y =tet + 2e2t + 1  To Find: Derivative of above

Q: Find of the function given implicitly and evaluate the derivative at the given point. y = sin ( 8x+…

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Q: Let e - v = 1. Find each derivative. du dv (a) dv (b) du (c) Based on your answers to parts (a) and…

A: eu2-v-v=1

Q: Calculate the first numerical derivative of the following equation with the values xo = 1 and y o =…

A: Given function is fx,y=ex3y−sinx,  x0=1 and y0=15.6 for Δx=Δy=0.1 We have to find the first…

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: What is the first derivative of the function h(t) = t/2t – 3

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Q: 13. Find the derivative of the following functions and simplify the answer 10z + Va y = (a) 8x2-7 et…

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

A: We will find f'(x) using the product rule and the chain rule.

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

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Q: What is the derivative of (9x² + 14)2 (20x2 +11a- 15)3 123 e y = with respect to x? Hint: Take the…

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

A: Given fx=x+223

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: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOLUTION): 2 X = 2…

A: First, evaluate the first derivative dydx (y'). To find y', determine the dxdt and dydt.…

Q: if x=t^2+1 and y=t^3, then the second derivative is?

A: x=t^2+1⇒dx /dt​=2ty=t^3⇒dy/dt = 3t^2​

Q: Determine the value of the derivative of the function stated below, at x = 1. d "2х-1 4 dx \ x+2

A: The given function is: f(x)=2x-1x+24

Q: Evaluate the second derivative of mq4.5.png os (bVx³) f(x) = a ln sin(cx2) if a = 21, b = 0.5, and c…

A: Given that, f(x)=alncosbx3sincx2a=21, b=0.5, c=5Substituting the values of a, b and c, we…

Q: dV E = dx d(a+bx) E = - dx E = -(b)

A: Consider  V=a+bxE=-dVdx

Q: Find the 127th derivative of (1 t a*) 16 at r 0.

A: we need to find 127 derivative of given f(x) so we need to apply product rule

Q: Q2/ Find the derivative 1. sin(xy)= of each of the following functions:- 2. y =(Inx)³ 3. y=cos (sin…

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Q: (1) For each of the following, compute the desired derivative. (a) If g(x) = 5x® – 22 + 7, compute…

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Q: In (4x) Find the derivative of y with respect to x if y = sin (8 e') dt.

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Q: 4. D, (x-2)(2x +3) 5. D, (e")

A: We know that, Dx(ex) =ex Dx(xn) =nxn-1

Q: Find the derivative of the function.

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Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: Solve for the derivatives of the following functions with complete solutions. a. y = In (5x²) b. y =…

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

Q: 3. Find the derivative of y = | (12 +1) dt.

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Q: Find the derivative of each of the following: (a) (x – 1) sin 2r, - (b) sin 2r T-1 (c) e2" sin 3x…

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Q: Find the derivative of y with respect to the independent variable. 20) y = 7cos TO A) -17COS TO In 7…

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Q: Find the derivative of the following:  R = (q^2 + 1)^4 y = ln(5t + 1)

A: We have to find derivative of given different functions ,Given different functions are

Q: 18. Up to what derivative is the derivative of y = x6 + 2x5 - 4x4 + 7x³ becomes 0.? a. yv b. yu c.…

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