-at f(t) = 5e"t – 5e

Q: If dy dt y. 1 - et and y = 0 when t = 1 find

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Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: A particle is moving along a line, whose directed distance from its origin is given by the function…

A: f(t) is a distance function.

Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

A:

Q: f(x.y) =e^sin(y) + In(xy) ; әз of Әхд-у

A: Given: fx,y=exsiny+lnxy To find the partial derivative of ∂3f∂x∂2y Partial differentiation: Partial…

Q: Let y=x2+2x. Compute Δy and dy at x=3 if dx=0.2. What is the difference between Δy and dy? That is,…

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Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: The function g(t) = \t| is differentiable at 0. True False

A: Given that g(t)=|t|We can write it as:g(t)=t   , t≥0-t , t<0

Q: Find dy/dx of the following function using Chain Rule. y=(x3 + 3)5

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Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

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Q: -2r²+2x+1 ev dy at x = 0. Find the equation of the tangent line to the graph of F(x) = sech z

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Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

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Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: Q3) Find dy/dt of the function y = cos (5sin (t/3))

A:

Q: 3. Let X(t) = t2W (t) – 2 f sW(s)ds, Is X(t) a martingale?

A: X(t)=t2W(t)-2∫0tsW(s)dsWe know that, X(t) is a martingale, if,EX(t+1)=X(t)

Q: If s = f(t) denotes the position of a particle at time t, the derivative f'(c) is the of the…

A: Solution:Given      If s=f(t) denotes the position of a particle at time t, the derivative f'(c) is…

Q: 1losamlov ç5x3-1 Differentiate the function g(x) = [°*¯'sin t dt. -3

A: We have to differentiate the given function.

Q: find out wheher the function s the selution o the differential gurticn 300 2e Oy= जू - 194 + 243D 0…

A: This question is related to differentiable equation.

Q: dy t² +3 21. Find 9 if y = In dt /1-t,

A: We need to find derivative of given function with respect to t

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: a particle moves along a curve x = t^3+1, y=t^2, z=2t+5 , where t represents the time . its velocity…

A: Velocity is obtained by differentiating the position function

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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Q: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

Q: (a) f(x) = e" centered at r = 0.

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Q: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: Find the differential d3y of the function y=1/√x.

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Q: D-the derivative is y = In In (VW) 1 +

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

Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: Find the gradient ∇f of the function f given the differential. df=2ye^xdx+xe^xdy   ∇f=

A: Note that            . Here, df=2yexdx+xexdy. So, here we have fx(x, y) = 2yex and fy(x, y) = xex.

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: Find the differential of the function f(x) = (x+4)^(1/2) dy =

A: Find the differential of the functionf(x) = (x+4)^(1/2)

Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: a) If d'r = 3, when t = 0 we have dt? dx 0 and x=0, what is x as a function of dt t?

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Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: If x=t² - 5t and y=1-61 , then dy at t=1 is dx

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Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

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Q: dx Suppose y = x4 – 2x + 1, and both x and y are functions of t. If dt when x = -1. dt = 2, find 12…

A: Given Data The equation is y=x4-2x+1. The derivative of x with respect to t is dxdt=2. x=-1.…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: Find dy/dx of the following function using Chain Rule. y=(-3x5 +1)3

A: we use chain rule for differentiation y=(-3x5 +1)3 dy/dx =3(-3x5 +1)2(-15x4) dy/dx = -45x4(-3x5 +1)2…