4) If F(x)= } d, then F'(x)- sin t

Q: y = In (x* + 5)³

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Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

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Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Find the derivative of f(x)=sin sin(5x

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Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

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Q: What is the derivative of x sin(x) at the point (6,5)? 2 O 1 O-1 O None of the above

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Q: 28. The derivative of In(x sin x) is 1. 1 + cotx а. b. C. d. tan x +x - +x sinx

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Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

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Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

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Q: 14) The derivative of y = cscx sin x is y = 0 A) True B) False

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Q: y = (Arccos 3x³)³

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Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

A:

Q: Choose the derivative of sin (x). - 1 1 1+ x2 1 x2 | 1 1+ x2 1 xVx2 1 - 1 V1- x?

A: It can easily find the derivative of function

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

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Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

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Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

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Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

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Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

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Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

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Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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Q: 3/ By using the definition of derivative, proof that tan x = sec? x. %3D dx

A: By definition of derivative , f'(x) = d(f(x)dx= limh→0f(x+h) - f(x)h L Hosital's Rule :When limit is…

Q: y=ln(sin(X3-1))

A: Detailed explanation is attached below.

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

A:

Q: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

A: we are given the function is  f(x)=1+sin2x2cos3x

Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

A:

Q: Determine the first derivative of the ff. function a. y = 400(2)*+3 sin 3x b. y = Vxe2x cosx…

A: Given1) y=400(2)x+3sin3x2) y=xe2xcosx3)y=1+ln(3x2)1+ln(4x)We need to find the first derivative of…

Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

A:

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: Find the derivative of: sin sin(2x) sin sin(x) + cos (2x) cos(x) ans: -sinx solution?

A: We will use the formula cosA*cosB+sinA*sinB= cos(A-B) , with A=2x and B=x and simplify.

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: The value of the second derivative of at its point of inflection is A less than zero B equal to zero…

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Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

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Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: 4. If y = x cos x determine the 5th derivative. [y6) = (60x – x³) sin x+ (15x? – 60) cos x] |

A: