If f(x) = }(e3 + e-32), calculate f'(1). If f(x) = 32*, find f'(x). Find f'(0) for the function f(x) = sin² x + cos 2x.

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: Differentiate y = /sin(x² + 3)cosx

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Q: find the derivative of the log functions: y = ln(x√x2 – 6) f(x) = ln(2x/x+1)

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Q: The derivative of y = 2 ln ⁡ x − ln ⁡ x 3 is

A: The given function is, y=2lnx-lnx3

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

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Q: 4. By implicit differentiation , find the 1st derivative of x3 + y3 + 6xy = 0

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Q: 29. Find the 5th derivative ofy= sin2x

A: 29. Given function is, y=sin2x. The first derivative of y is, y'=ddxsin2x=cos2x·2=2cos2x   The…

Q: 1. Find the first derivative " if y = x sin 27x . dx

A: Given:  y=x sin 2πxTo determine the firstderivative.

Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: Find the derivative of y=cos4 x sin4 x Ans: 1/2 sin3 (2x) cos cos (2x) solution?

A: We simplify the given expression using the double angle property

Q: 2.) Find 1st derivative of y = e-'In (x-1)

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Q: Find the equilibria of the differential eq

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Q: derivative of y = arctan(x2+ 3)

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Q: 18) Find the first derivative of y = 1 -sin² x - 4

A: The given function is: y=14sin2x

Q: Find the derivative of ln(2x2)+ln(2x)+1/3 where x=1

A: Given,           The derivative of  ln2x2+ln2x+13 where x=1

Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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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: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: Find the second derivative of g(x) = sinh(x) cosh(x)

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Q: In 2x y = - cos x

A: ddxln 2xcos x= ddxln 2x . cos x - ln 2x.ddxcos xcos2 x= 12x. 2. cos x - ln 2x.(-sin x)cos2x= cos xx…

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

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Q: a the derivative of h(x) = ln + 2 x5 et |

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Q: 5. y=x3 Find derivative ldv 4.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: FInd the derivative of f(x) =ln 1+ex/1-ex

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Q: Find the derivative of f(x) = –4 ln (5 cos (-4x))

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Q: Find the derivative y=ln(2x^3+6x-1)^3

A: y=ln2x3+6x-13 take derivative y'=ddxln2x3+6x-13 y'=12x3+6x-13ddx2x3+6x-13

Q: 4 Find the first derivative of y = In X +

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln3/x

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Q: Using the Chain Rule, compute the first derivative of sin 1–x.

A: chain rule Let f(x) = g(h(x)) And let u = h(x) Using the above, function f may be written as: f(x) =…

Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: What is the derivative of the function  x^8(ln(x)), and what can I substitute for x to make the…

A: We have to find derivative dy/dx and point where dy/dx =0y is given below:

Q: find the first derivative of the function. F(x)= (1+sin2x/1-sin2x)^3

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

A: Detailed explanation is attached below.

Q: Va2-x² Y=Arc sin + a

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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: he first derivative of f(x) = ln(5X4 - 6x) will be

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

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Q: Find the derivative of  f (x) = ln( ln (ln 3x))

A: To find the derivative of f(x) = ln( ln (ln 3x)), differentiate f(x) with respect to x.

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: 5. Find the derivative of --( 1 + sin 0 cos 0

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Q: is the derivative of In

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Q: Find y'' by implicit differentiation. 5x2 + y2 = 4

A: Implicit differentiation

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: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

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

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Q: 5-cos x 3) f(x) = 5+sinx foo

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Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows