Given u(t) =< 6t?, 1t, sin(t) > and v(t) = < 1, cos(t), In(t) >. Find the derivative of u(t) • v(t) at t = 6. Give your answer correct to two decimal places. Answer:

Q: 1. Determine the derivative for y = | a. d. 中正中正 中正中正

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Q: find the derivative of y with respect to x, t, orθ, as appropriate.

A:

Q: Find the derivative of the following function. y (In ]x + 4|)7 dy

A: Differentiate w.r.t to x

Q: Find the derivative of the function.

A: Given, To evaluate derivative

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

A:

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

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Q: Find the first order derivative with respect to y of the function u = log(x + x² – y2)

A: Using derivatives.

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: Find the requested higher-order derivative for the given function. d3y of y = x" - sec(x) dx3

A: Given that y=x11-secx and we have to find third order derivative of y with respect to 'x' that is…

Q: Eョ2 T -(X子 ノ = (X)J fi(3)

A:

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 * T (x) = Va + 9 Væ? 2.

A: Given T(x)=x+9x73-2x25…

Q: Find the first derivative of the function (xy)* = e.

A: Explanation of the answer is as follows

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

A:

Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: Find the derivative of y with respect to x if y = (13x - 26x+26) e -8x y =D %3D

A: Explanation of the answer is as follows

Q: Find the derivative of the function f(t) = te-t. f'(t) =

A:

Q: Find the derivative of the function. %3D y = log |3- 5x| dy

A: Here , we will differentiate y  with respect to X  .

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, 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.

A:

Q: Find the derivative of y with respect to x if y = (12x - 24x + 24) e - 3x. y' =D %3D

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

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

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

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Q: Find the derivative of the function. y = cos(a + x*) У (x) %3

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (t3/2) + √t

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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: 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: Find the derivative of the (e) h(x) = e5 sin (Væ) + a° sec ()-

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: find the derivative of y=1/b²[a+bx-aln(a+bx) where a and b are constants

A: Derivative of function

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 f (a) = e" (x² + 2).

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Q: y = V5х+7

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Q: Find the derivative of the function. g(t) = ln t/t2

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Q: The third derivative of the function y = e2a with respect to x is

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the derivative of y with respect to x for y = sinh - 1 ' (11/9x).

A: From the given problem:   y=sinh-1119x...(1)   Now simply write as: 119x=11· 3x=33x   Substitute…

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

A: Given :

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 the function. y = ln(t + 1)2

A: On simplification, we get

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

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Q: Find the derivative of y with respect to the given independent variable. e* cos' x (1) y= x+1

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Q: 2. Find the derivative of h with respect to u if h = n²u

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Q: Y= tan ot

A: