d the derivative of f. (x) = tan? x ich is the correct answer? x) = 2 tan x sec x) = -2 tan x seo? x x) = 2 secx

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

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Q: Consider the function f(x) whose second derivative is f''(x) = 8x + 6 sin(x). If f(0) = 2 and f'(0)…

A: Given  f''(x) = 8x+6 sin(x),  f(0)=2,  f'(0)=4 We have to find the value of f(3).

Q: 1. Write the equation of the line tangent to f (x) =1 + e*sin(2x) when x = 0. %3D %3D

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Q: Assume that y = sin'x is a differentiable function of x. By differentiating the equation x= sin y…

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Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = cos x/2

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Q: Consider the function f(x) whose second derivative is f"(x) = 6x + 3 sin(x). If f(0) = 4 and f'(0) =…

A: Given,

Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: Calculate the derivative of: '(14z) cos f(1) = sin (14x) r(e) =O

A: Given query is to find the the derivative of f(x).

Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: Find the derivative of each function. し-X a) f(x)=7x² tanx -1 %3D u du ol x v du そar1 (x)2x tan…

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Q: h(x)= cot r11- tan"x

A: Given, hx=cot-11x-tan-1x We have to find h'x.

Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 9 sin(x). If f(0) = 4 and f'(0)…

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Q: compute the derivative. f (θ) = eθ (5 sin θ − 4 tan θ)

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Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 2 sin(x). If f(0) = 3 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 6 sin(x). If f(0) = 3 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If f(0) = 4 and f'(0)…

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Q: The derivative of the function y = tan-1 Vx2 – 1 + csc¬1 x, where x > 1 is: |

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Q: 2. Using the definition of derivative, prove the following: 1 (a) f^(x) = if f(x) = Vx (b) y= sec? x…

A: To find the derivative using definition

Q: Consider the function f(x) whose second derivative is f''(x) 8x + 3 sin(x). If f(0) = 4 and f'(0) =…

A: Given : f"(x) = 8x + 3 sinx, f(0) = 4, f'(0) = 4,    To find : f(5)?

Q: Question * The derivative of the function y = x(tan¬1(3x))² is:

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Q: Find the derivative with respect to the independent variable. f(x) = 9 cos x - 2 sin x f'(x) = D %3D

A: We have to find derivatives of function: fx=9cosx-2sinx We know the derivatives of trigonometric…

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: What is the third derivative of f (x) = a + cosæ?

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Q: Use the quotient rule to show that the derivative of cot(x) is − csc2(x). That is, prove that d/dx…

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Q: What is the equation of the line tangent to the curve e' + cos(x) = 1 at the point (,0

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Q: Consider the function f(x) whose second derivative is f"(x) = 6x + 5 sin(x). If f(0) = 4 and f'(0) =…

A: Using integration &amp; given condition.

Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: Consider the function f (x) whose second derivative is f"(x) = 10x + 8 sin(x). If f (0) = 2 and…

A: Given function is

Q: Compute the derivative: tan-'(ax) (bx) (a) y = sin='(x²) (b) y = (tan-1 r)³ (c) y = sin

A: (a)   Differentiate the given equation with respect to x, dydx=ddxsin-1x2=11-x22ddxx2=2x1-x4

Q: Find the second derivative of 1. F(x) = tan(2x) 2. F(t) = e^t sint

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

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Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 6 sin(x). If f(0) = 2 and f'(0) =…

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Q: Find the equation of the tangent line to f at x = a. f (x) = 3 − 4x,             a = 2

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Q: Find the derivative of f(x) and solve for x sinx a. f(x) X = 6. b. f(x) e* sinx X = 0 COSX c. f(x) X…

A: Given: (1) f(x) = sin x / x  at x = π/6  (2).  f(x) = ex sinx at  x= 0 (3).  f(x) =  cos x / ex   at…

Q: 1. If f(x) = (2x)cosx, then f'(x) =?

A: Dear student as per our rule in one session we can only solve one question please post the other…

Q: What is the equation of the line tangent to the curve e + cos(x) =1 at the point.0 A y=x+ B y=0 y=x-

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Q: d/dx[tan^-1(x)]=1/1+x^2 prove the derivative

A: Solution

Q: Consider the function f(x) whose second derivative is f''(x) = 5x + 7 sin(x). If f(0) = 2 and f'(0)…

A: Given :f''(x)=5x+7sin(x)

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 3 sin(x). If f(0) = 3 and f'(0)…

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Q: Find the derivative of the function x3 y = / 9vi sin(?) dt. %3D

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Q: Consider the function f(x) whose second derivative is f''(x) = 10x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Given, f''(x)=10x+8sinx(x) After integrating the above equation,…

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinaxdx=-cos(ax)a+c ∫cosax dx=sin(ax)a+c ; where 'c' is an integration…

Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 7 sin(x). If f(0) = 2 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f" (x) = 9x + 3 sin(x). If f(0) = 3 and f' (0)…

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Q: Find an equation of the tangent line to the y = sec(x) – 6 cos(x), P = 3 y =

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Q: What is the equation of the line tangent to the curve e+ cos(x) =1 at the point .0)? A y=0 B y=x -…

A: Explained below

Q: Find the equation of the tangent line to y = g(x) =x? + 2 cos(x) at the point where x= 2

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Q: The derivative of the function () y = In is: tan x,

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Q: (a) Find the equation of the tangent line to the curvey 2 sec x – 4 cos x at the point (÷, 2)

A: Tangent line to the curve y=f(x), where f(x) is a function of x at point x0, y0is given by:…

Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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