The rate of change of the temperature of an object is given by T (t)=t·eª -0.1t min (a) Use the u-substitution method to find a formula for the temperature T(t) knowing that the initial temperature of the object T(0)=20°C. Check your answer using differentiation.

Q: Find the derivative of the function = etan(e) y' =

A: y = etanθdydθ = detanθd(tanθ) × d(tanθ)dθdydθ = etanθ.sec2θ

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A:

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A: Given f(x,y,z)=esin(x²+y²)/z To find del²f/delx²

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Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: Using implicit differentiation, dy for the dx equation x* + y* = 10 is x3 .4 y3 yt

A: According to question, Given equation,x4 + y4 = 10

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Q: ln(x+(x2 −16)^(1/2)) Find the domain and the derivative of the function.

A: Given, function is

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: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

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Q: Find the derivative y = (2x – a) (x² + e-")

A: We havey= (2x-x3)(x2 + e-x)

Q: 2) Find the first derivative: a) y = cot * (3x² +7)

A: Differentiate wrt x

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Q: A town library estimates that, when the population is x thousand persons, approximately y thousand…

A: A town library estimates that, when the population is x thousand persons, approximately y thousand…

Q: Using implicit differentiation, for the equation z5+y = 12 is .

A:

Q: Using implicit differentiation, for the equation z° + y° = 9 is

A: The given function is: x6+y6=9

Q: Using implicit differentiation, for the equation a +y = 10 is

A: This question is related to implicit differentiation, We will solve it using given information.

Q: Find the equation of the line tangent to the graph of f(x) = (In x)? at x= 8.

A: f(x)= (lnx)2

Q: Find dy/dx by implicit differentiation 9x2y + 5y?x = -9 9x dy/dx = 5y Need Help? Read It

A: Differentiate wrt x

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A: Find your answer below

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A: Given curve y2+xy-x2=11 at the point (1,3)

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A: The given function is s(t) = –16t^2+96t.

Q: Using implicit differentiation, for the equation z5+y = 12 is

A:

Q: Find the derivative for x+1 a)f(x)=- x-4 b)f(x)= sin' 2x Show the work on your notebook, take a…

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Q: 5. y³ = 4(y + x²)

A:

Q: Find the derivative of the xy+4x-(1/y) = 0.

A: →dxndx=n xn-1→duvdx=udvdx + vdudx

Q: 4 a. Use implicit differentiation to find the derivative dy/dx of the given function. b. Find the…

A: The objective is to find the derivative and slope at the point .

Q: Find the derivative of the given function at a given number 1. y=3x - 2 at f'(1) 2. y=x² -1 at f'(2)…

A: Find the derivatives at points. 1. y=3x2-2 for f'1. Apply derivative law: u±v' =u'±v'.…

Q: y = e* arctan x y = arccsc (e*) ICCSC

A:

Q: Find the second derivative of the function. 9. g(x) = x-1 10. h(x) = sinx = (x)6

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Q: (a) Find the derivative at x = −1. (b) Find the second derivative at x = −1.   h(x) = 2x4 + 8x3 +…

A: (a) The given function is

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A: Solved below...

Q: 10. Solve for the derivative of y IMPLICITLY 22 + Væ³ + 2y= y²

A: Note: According to our expert guidelines only first individual question is to be answered, kindly…

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A: I use product rule and chain rule to solve this derivative

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

Q: 1 Find the derivative of the function : ƒ(x ) = V |2x + 3

A: The given function is: f(x)=12x+3 Let, u=2x+3. So, f(u)=1u=u-12 and u=2x+3

Q: (a) f(x) = (3x² – 5x + 8)35 (b) f(x) = cos(27.x)

A: First I have written the chain rule and then using it find the derivative of given functions.Also…

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Q: Given the curve defined by the implicit equation ° – 7x + y* = 16, find the derivative of y with…

A: given x3-7x+y4=16differentiating with respect to x on both sides we get…

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Q: c. Find second derivative implicitly for y + 2Re *y = 3R.

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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: Given x3 + y3 = 9xy, y is a function of x. Show that the point (2, 4) lies on the curve above curve…

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