Find the derivative of y with respect to the independent variable. y = 10cos T) -.... A. - 10coS TO In 10 sin a0 B. - 10cos tO In 10 sin rÐ C. 110cos TO In 10 D. 10cos TO

Q: Find the partial derivative of the function with respect to each variable. 28 h(p,p.0) = p cos p sin…

A: The partial derivatives of the given Function is given as

Q: 3. a. -2 s = cos ¹(sin z) b. 1 C. -1 d. 2

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Q: Let y be defined implicitly by the following equation as a function of x and z : eXZ – sin(rxz) –…

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Q: 1 R(t) = 2 sin(t) – 4 cos(1)

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Q: 5. Determine the equation of the tangent line to (a) r= 2 sin e at = (b) r =1+ cos 0 at 8 =

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy Find the first…

A: Given that y is a function of x defined implicitly by the equation  siny=4x+xy

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

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Q: Find an equation of the tangent line and normal line to the curve at the given point for the…

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Q: Find the indicated derivative: d/dt ((e^t ,e^(2t),e^(3t)) X (sin(t),cos(t),tan(t)) )

A: We have to Find the indicated derivative of ((e^t ,e^(2t),e^(3t))(sin(t),cos(t),tan(t)) )

Q: 2 5. x=- 1+t2 2 y=, t(1+t?)

A: Given: x=21+t2, y=2t(1+t2).

Q: Determine the equation of the curve whose tangent line at any point (x, y) is e*- cos x and passes…

A: The curve whose tangent line at any point x,y is ex-cos x and passes through 0,4

Q: Calculate the derivative indicated in the figure below

A: rs=s, 2s, s2

Q: Evaluate the following derivatives.

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Q: Find the given higher-order derivative. f (4)(t) = t cos t, f (5)(t)

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Q: Find the derivative of y with respect to x in the following equation y = 1¹ where u = 1-z O x² O-x²…

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Q: Find the derivatives of the following functions. F(z) = 3 + cos(2z −1

A: Given :   f(z) = 3+cos2z-1

Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k.

A: Derivative of r(t) = cos (8t) i + sin9(t) j + tan (6t) k

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: The exact value of the slope of the tangent line to the graph of the curve r = 5 + 4 cos(0), at e =…

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Q: Compute the derivative of the given function. g(t) = 2t*e' – 4 sin t cos t g'(1) =

A: on doing differentiation with respect to t we get

Q: Find the derivatives of the following function. sin (ax +b) (cx +d) Cos

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Q: Which of the following is the slope of the tangent line to f(x) = cos(ax), a ER at x = T? O-a O-1 O…

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Q: Find the slope of the tangent line of the function y = In (x) at x = e2 O1/e? 4/et O 1/e* O 2le2

A: Topic = Derivative As per guidelines, At a time only one question can be answered out of different…

Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy Find the first…

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Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: Assuming that y is defined implicitly b equation x2 – y? = 17, the derivative (7, 12) is O 0.58 O 38…

A: We have to choose the correct answer from the given option according to the given condition

Q: Find the derivative of y with respect to the independent variable. y = (In 20)" Select one: A. T(ln…

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Q: Find the derivative of y with respect to x in the following functions: y= Ju +2u and u x2-3

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Q: Find the derivative of y with respect to x in the following function at (1, 1/3) u? y = u' +1 and u…

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Q: d -y(x) if e²-y = sin a d.x

A: We will solve the following

Q: What is the equation of the line tangent to the curve e+cos(x) =1 at the point ,02 + cos Ay= y=x-…

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Q: Find the derivatives of the following. 1. y= sin (e**+ 2x +5)

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Q: Find the derivative of y with respect to the independent variable. y = (In 20) Select one: A. T(In…

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Q: Find the derivatives of the functions defined as follows :

A: Given, y=3 tan14x+4 cot(2x)-5 csc(x)+e-2x

Q: Find the derivative with respect to the independent variable. f(x) = cos ? (8x2 - 1) f'(x) = D %3D

A: Given expression: fx=cos28x2-1 In such type of problem we will apply function of function rule: If…

Q: Which of the following functions has a derivative at x = 0? I. y = Vx² – 1 II. y = x|x| III. y = Vxª…

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Q: 1. Find the derivative (dy/dx) of the following functions: c) cos y + cotx = xy d) (3xy + 7)2 = 6y…

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Q: B. y = tan (x²+ 5x-2) %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the derivatives of each of these functions. a. y = (x¹+csc(z)) ³ b. y=sin(z) sec(41) c. y = csc…

A: Note - As per our guidelines we have to answer first three sub parts if multiple subparts are posted…

Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Find the derivative and simplify: y = cotVt - 1 1 2tvt - 1 1 2t/t -1 tVE -1 1 tvt-1 QUESTION 9 SLL…

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Q: Which of the following is the slope of the tangent line to f(x) = cos(ax), a E R at x = T? 1 а 1 а

A: Given equation is f(x)=cos(ax) at x=π Find the slope of the tangent line

Q: Find the derivative of each of the following: (a) (x – 1) sin 2r, - (b) sin 2r T-1 (c) e2" sin 3x…

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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: H.W Ex.(8) Show that the functions f(x) = sin' () and ga)=2 tanv メ+) have the Same derivative.

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Q: Find the derivative of y with respect to the independent variable. 20) y = 7cos TO A) -17COS TO In 7…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: Consider the curve x = ey. Use implicit differentiation to verifythat

A: Given: x=ey ;Take log on both sideswe get,  log x=log…