The brightness b of the sun (in watts per square meter) at a distance of d meters from the sun is expressed as an inverse-square law in the form where L is the luminosity of the sun and equals 3.9 x 1026 watts. 477d2 What is the derivative of b with respect tod at the earth's distance from the sun (1.5 x 101' m)?

Q: Use the Product Rule to compute the derivative: # (² + 1)(t +9))|t=13 d ||

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Q: Find the derivative of the function

A: Given expression

Q: Evaluate the derivative of  the image  if a = 90 and b = 0.5 at x = 4 using CDA  with Δx =0.11.…

A: For the given values of a, b and c, f(x) is given by f(x)=90cos0.5xx2

Q: Use the Power Rule to compute the derivative. d „0.25 da f'(x) =

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Q: 8. To find the derivative of y = cot* (2x), which of the following is the appropriate value of u? A)…

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Q: Use the Power Rule to compute the derivative.

A: The power rule of derivative is given by: ddxxn=nxn-1

Q: # 41) Use the definition of derivative to find f(r) and "(r) for (r)= 1+ 4r- r

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Q: 2020 at 1T:36 PM Find the derivative of the following function using the rules of differentiation:…

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Q: (c) Find the derivative of nh (cosu). Where n is 482

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Q: Find the derivative of y with respect to the independent variable. 6- e y=t O A. (6- ers-e O B. (5-…

A: The derivative of xn is given as,ddx(xn)=nxn-1

Q: Solve for the derivative of the following and simplify if possible. h(t) = t3 - t2 sin t

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Q: If an object is dropped from a 674​-foot-high ​building, its position​ (in feet above the​ ground)…

A: (a) The given function is dt=-16t2+674. Differentiate the function with dt=-16t2+674 by the power…

Q: Use the Quotient Rule to find the derivative of the function. Re) = cos(e) f(t) f'(E)

A: Given f(t) = costt5wktduvdt = vu'-uv'v2

Q: Evaluate the second derivative of  the image if a = 380 and b = 0.4 at x = 5 using BDA  with Δx…

A: The finite difference formulae can be used to calculate the derivatives of the functions. The…

Q: Use the quotient rule to find the derivative. Simplify the result. d [ 6/I dx 3x – 4

A: given                                                  ddx6x3x-4 Quotient Rule of differentiation…

Q: Use the product rule to find the derivative of ?(?) = √?(?2 + 8). The spirit of the  problem is to…

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Q: If an object is dropped from an 867-foot-high building. its position (in feet above the ground) is…

A: height of the building = 867 footposition of object d(t)=-16t2+867a)      d1(t) = -16 ×2×t+0…

Q: A stone is launched vertically upward from a cliff 384 ft above the ground at a speed of 32 ft/s.…

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Q: Use the rules of differentiation to find the derivative of the function

A: First note the following rule of differentiation (f(x)+g(x))'=f'(x)+g'(x). Another rule that will be…

Q: 3. Find the derivative of each of the following functions. Justify your answer. (a) f(x)= (b) y e I…

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Q: 46 Find the derivative of f (t) = (8t³ – 5t2 +1)* f' (t) =

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Q: 2 5. x = - 1+t2 2 y= t(1+t²)

A: To find the second derivative of parametric equations, x=21+t2 and y=2t(1+t2), use the formula,…

Q: (х? + 2х + 3)(5—х) 10. g(x)= Зх + 2

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Q: Suppose y=4V X +6V x. What is the value of its derivative at a=64? Write the answer in exact form,…

A: The function is given by y = 4x+6x3 To evaluate: The value of dydx at a =64

Q: ind the derivative of the function y = (x+ 8 sinx) (1+ 14x), and simplify the answe

A: Given : y =(x+8sin-1x ) ( 1+14x)

Q: derivative

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Q: What is the value of the derivative of y=sin(x)cos(x) when a = 2? Write the answer in exact form, an…

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Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…

A: Given that y=x2+4x−5. We have to evaluate the first derivative of y=x2+4x−5 at x=0 using a value of…

Q: A stone is launched vertically upward from a cliff 48 ft above the ground at a speed of 32 ft/s. Its…

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Q: nd the derivative of the function. (6 – x)5/4' x4/5 y = In

A: We will find the derivative.

Q: Determine the second derivative of H(t)=cos?(7t)

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Q: V(x) = In(sin(x) – cot(x))

A: The chain rule of differentiation is dydx=dydu×dudx. The given function is Vx=lnsinx−cotx.

Q: Pind The second derivative of the following function F(X)=e

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Q: (b) Use your answer from part (a) to evaluate the derivative. (ӕ — 5)30 In d dx V (2а — 7)34 -

A: first, simplify the function ddxlnx-5302x-734 =ddxlnx-5302x-73412 =ddxlnx-53022x-7342…

Q: 13. Find the derivative of the following functions and simplify the answer: 6x+ VE (a) 7x2 – 1 e…

A: As we know that the derivatives of:-  the Quotient Rule:  fg'=f '·g-g'·fg2 Apply the Sum/Difference…

Q: 3. y= In (*+1), (x+2)3 (x+1),

A: 3. The equation is  y=lnx2x+1x+23

Q: 4. y = 6+4 vx csc x 5. R(t) = 2 sint-4 cost

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Q: What is the derivative of ( 6 t cott−4e^t)

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Q: Find the derivative of the function. F(t) = 5t sin(mt)

A: To find the derivative of the given function f(t) we use product rule for derivative, Since f(t) is…

Q: Find the derivative of the function. Simplify and express the answer using positive s = [(2 – t2)(?…

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Q: Find the derivative with respect to x if f(x) = (9x² – 18x + 18) e*. The derivative with respect to…

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Q: Solve for the derivative of the following functions. Write your answer on a separate sheet of paper.…

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Q: c) Find the derivative of nh (cosu). Where n is 482

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Q: Use the product rule to find the derivative of (82° – 3x*) (7e" – 1) Use e^x for e". You do not need…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: t+1 5. V(t)= t+4

A: By definition of derivative we have to follow basic of derivative that is  F'(x) = Lim h->0…

Q: Use the Product Rule to calculate the derivative.

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Q: 4) Use the quotient rule to find the derivative. Simplify the result. d [3+7e* dx | 6e* + 5

A: given that, dds3+7es6es+5 we have to find the derivative using quotient rule.

Q: Use forward-difference formula to evaluate the first derivative of y = x² + 4x – 5 at a = 0 using a…

A: The forward difference formula is : f'(x)=f(x+h)-f(x)hWe have to find the first derivative of…

Q: Calculate the derivative of the following functions

A: We have to find the derivative of the function y=p+32sinp2.

Q: Solve for the derivative of the following and simplify if possible. f(w) = tan w sec w

A: We can find the derivative as below using the product rule