B. Derivatives of Trigonometric Functions Using the formula find 6. y=tan Vx2 – 1

Q: QI/ answer of the following 1- Find y" if y= cscx 2- Find if y = 3- Using implicit differentiation…

A: 1) The given function is y=csc x. Evaluate the second derivative of the given function as follows.…

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: To find: The equation of tangent to the curve and also find d2ydx2. Given: The functions are x=cos…

Q: Find the derivative of the trigonometric function. g(t) = 5 cos2t

A: g(t) = 5 cos2t We need to find the derivative of the trigonometric function:

Q: B. Derivatives of Trigonometric Functions dy Using the formula find dx 4. y=sin (x² + 3x + 1)

A: This is the simple derivative problem where d/dx (sinx)= cosx is used

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0S0< x.…

A: Given :           r=6 cosθ

Q: 3. Given the equation y = In(cos(x)): What is dx/dy? secx -seox -tanx -cotx None of the choices.

A: I am attaching image so that you understand each and every step.

Q: d all points on the graph of the function f(I) = 2 sin z + sin z, 0 <I< 27 at which the tangent line…

A: Given query is to find the points where tangent is horizontal.

Q: The exact value of the slope of the tangent line to the graph of the curve r = 9 + 8 cos(e), at e =…

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Q: 4. y = csc x cot x 5. f(x) = cos 2x + sin² x sin 3x 6. у3 4+5 cos(2x)

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Q: 1. Find the derivative of the following trigonometric functions a) y = x sin(x) + cos(x) b) y =…

A: Given the trigonometric function

Q: II Find the second derivative(y") of the following functions and simplify the final results. 1.…

A: Formulae used: ddxarcsinx=11-x2ddxxn=nxn-1ddxx=1 Quotient rule of differentiation: pq'=qp'-pq'q2…

Q: 39. f(t) = t² sin t cos t 41. f(t) =

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Q: Find the equation of the tangent line to r = sin3θ  at θ = π/6

A: The equation of the tangent line to a curve y = f(x) is: where m is the slope of the tangent line m…

Q: 1. cos(xy) + secy = 5

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Q: ind the derivatives and simplify answers: a). f(x) = tan-(e4"), (b). g(x) = x² + 2r³ cot-- In(1+x²).

A: ddx(arctan(e4x))We know that…

Q: Find the equation of the tangent line to the curve y = 4 sin x + 2 cos a at the point (0, 1/2). The…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: Equation of tangent is given by y-y1=m(x-x1), where m is the slope and equal todydx and (x1,y1) is…

Q: 6. y= cot Vx2 - 2x -1 7. h(x) = Sin Vx %3D

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Q: X= cos t, y= sin t; t= 6

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Q: C) Find the equation of tangent to the curve 4x +9yi = 36 at the point (3 cos 0, 2 sin 0).

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Q: 33. For what values of x does the graph of f(x) = x +2 sin x have a horizontal tangent? %3D

A: We need to find values for which the function have horizontal tangent.

Q: Find the derivative of the trigonometric function. g(t) = 9 (cos(πt))4

A: Given    g(t) = 9 (cos(πt))4 Differentiating with respect to t,g'(t) = ddt9 (cos(πt))4g'(t) =9 ddt…

Q: find an equation for the line tangent to the curve atthe point defined by the given value of t.…

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Q: Differentiate.   y  = Cos h -1(Sin h x)

A: Given inverse hyperbolic function - y = cosh-1sinhxUsing Chain rule, differentiating on both sides…

Q: 30 Find the real and imaginary parts of the functions (a) z²e2= (b) sin 2z Verify that they are…

A: We will use standard techniques.

Q: 2x y= Arccos(e)

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Q: e derivative of the trigonometric function. g(t) = 9 (cos(πt))4

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: Find the derivative of the trigonometric function. h(t) = 2 cot2( t + 2)

A: h(t)=2cot2(t+2)Here we use the concept of chain rule. Formulas ddxxn=n xn-1ddxcot x=-csc2x

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find an equation of the tangent line to the curve at the point corresponding to the given value of…

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Q: 1. H(w) = 2 cos(w) – 6 sec(w) + 3 H'(w) = %3D

A:

Q: Find the derivative, , for y = (x² – V)3 Find the derivative,, for y = csc Find the first and second…

A: Derivative of the following

Q: Find the equation of the tangent line to the curve 1 y = 3 sin z + 4 cos a at the point (0, 1/4).…

A: Given:     y = 1 / ( 3 sinx + 4 cosx ) Point: ( 0 , 1/4 )

Q: Find the derivative of the following functions. Show complete solutions, including trigonometrie…

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Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: 4 Y= 5/(sin3x +cos3x)

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Q: Function y=y(x) is given in the following implicit form: sinx+y/cosy+x  =1 1. Find y'= 2. Find…

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Q: Find the exact value. 3 S sin cos 2 0 x dx

A: Follow the procedure given below.

Q: For the following parametric equation x(t) = tan t and y(t = sect find the %3D tangent line passing…

A: The given parametric equations are  x(t) = tan t y(t) = sect The given point t = π3 xπ3 = tanπ3 = 3…

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Given,         x=t-sint , y=1-3cost , t=π3

Q: Function 1 t h(t) = sin t+=e 5 Point πT 1 I, -e 5 (a) Find an equation of the tangent line to the…

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Q: Find the indicated derivative. Then find an equation of the tangent line at the indicated point on…

A: Please refer the attached image for complete solution.

Q: Determine the derivatives of the following inverse trigonometry functions .1 f(x)= tan- Vĩ. .2 h(t)…

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Q: . Arcsin(x/y) = 4x + 3y

A: Solution :-

Q: d The derivative of the sine function is the cosine function: (sin x) dx = cos X

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Q: Calculate the higher derivatives. y = 7e¹ sin(t) (Use symbolic notation and fractions where needed.)…

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