Given u(t) = < lt, 7t, sin(t)> and v(t) =< 1, cos(t), In(t) >. Find the derivative of u(t) v(t) at t 8. Give your answer correct to two decimal places. Answer:

Q: Find the derivative with respect to t for the function y = 2/t.

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Q: B) Find the third derivative of the function: Y = +VX

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Q: find the derivative of y with respect to the givenindependent variable. y = t1-e

A: In this equation the independent variable is t So we will differentiate with respect to t

Q: F(2) = [*e*ax e' dt

A: We have to find derivative

Q: 2. Calculate the derivative of the following. B. Y= tan(x+ 5r-2) C. y=- (E +24) :(2-)

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Q: - 9x Find the derivative of y with respect to x if y = e dy %3D dx

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Q: Find the derivative of the following. g(x) (e2t + VE - t) dt g'(x)

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Q: b)Find the derivative of the function by using the derivative definition? ds if s dt 2t + 1

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Q: Find the derivative of the function.

A: Consider the provided function, ht=t2t3+22 Find the derivative of the function. Apply the chain rule…

Q: Find the derivative of the following function. fy) = e Yy" .....

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Q: Find the derivative of z=tan(e^-7w) dz/dw

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Q: Find the derivative Of g(t)=ln(e^-t+2t)

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Q: Use the Chain Rule to find the derivative of the following functions.

A: To find the derivative of y=1-ex4 using the chain rule. Solution: Chain rule of differentiation…

Q: What is the derivative of y = V(x? V(a2 – 1) (x + 1) ? -

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Q: Eョ2 T -(X子 ノ = (X)J fi(3)

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Q: 2. Calculate the derivative by first principles for the following: i. f(x)=Vx,

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Find the derivative of the function. z = (4 – t)(1 + t?) `

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Q: FIND THE SECOND DERIVATIVE OF THE FOLLOWING IN ITS SIMPLIFIED FORM. x = t/t-1 , y = t2/t2-1

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Q: Find the derivative. f(x)= | t lInt dt . e

A: Consider the function  f(x)=∫e extlnt dt

Q: Z = 1+x2 ; d'z/dx?

A: Given: Z = 21+x2 To find: The derivative, d2 Zdx2 in simplified form.

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = t (ln t)2

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Q: Find the derivative of y with respect to x if y = e¯1X. dy dx II

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Q: Given that h(x) = xi + what is the anti-derivative of h(x)? (Do not include the constant C'in your…

A: Anti-derivative

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y 2xe X- 2e X O 2xeX O 2xeX +…

A: Finding the derivative

Q: Find the derivative of the function g(t) = (e−t + et)3

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Q: Obtain the derivative of the function y y = (e*1) (In(2cos(x² – 4x))

A: The given function is: y=e3x+1ln2cosx2-4x

Q: Find the derivative of y with respect to x. y=log(base)5 e^7x

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3 2x +5 2. y=Va² +x?

A: Using three step rule.

Q: If z = (x + y) e and x = 6t and y = 1 – t, find the following derivative using the chain rule. Enter…

A: In this question we have to find the differentiation of z with respect to t.

Q: The derivative of the function y = x² In(x + 1) is:

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Q: Find the derivative of the given function. y =x² Vx-

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Q: Find the derivative of y with respect to t.   y=t(ln2t)^(2)

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Q: Find the derivative of y with respect to t. y = t(In 1t)2

A: The given function,  y=t ln 1t2

Q: What is the derivative of r(t) = ⟨ƒ(t), g(t), h(t)⟩?

A: we have the vector r(t) = ⟨ƒ(t), g(t), h(t)⟩   r′(t) is the derivative of the vector r(t)  The…

Q: Find the derivative of h(x) = e³ + Vx + lnx. I

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Q: g. y = x e 2x h. y = 4sin 2x

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Q: Find the derivative of the function. h(t) = 1 2 dt

A: We have to find the derivative of the given function.

Q: y = V5х+7

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Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

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Q: Find the derivative of f(t) = e+1

A: Given :

Q: Q2: - Find the second derivative of the following function at x = 2 1) y=+ V

A: ddx1x = -1x2 ddxxn = nxn-1 ddxx =12x

Q: h(t) = (e" +2)

A: given that h(t)=(e3t+2)5  So h'(t) = d/dt (e3t+2)5  h'(t) = 5(e3t+2)4 [d/dt (e3t+2)]  h'(t)= 15e3t…

Q: Find the derivative of F(x) = t°e' ln tdt.

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Q: Find the derivative of function ei, x#0 1 еx, f (x) = 0. at xo = 0 X = 0

A: Find the derivative of the given function.   Given: fx=e1x, x≠00, x=0

Q: Find the derivative of the function.

A: Given- gx=∫1cosx1-t23dt To find- The derivative of the above function. Concept Used- Using the…

Q: - 18x Find the derivative of y with respect to x if y = e dy %3D dx

A: We have to find the derivative

Q: Y= tan ot

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Q: Find the derivative of v(t) = te-ct Assume that c is a constant. v (t) =

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Q: Find the derivative of y with respect to T. Y=t( ln 10t)^2

A: Use the derivative of the form f = uv