Differentiate the given function: y = In(sinh(2 z)) a) О sinh(2 ¤) 2 cosh(2 ¤) b) O sinh(2 z) 2 cosh(2 z) sinh(2 r) d) O cosh(2 ¤) cosh(2 x) sinh(2 r)

Q: Match each function with its derivative. y dy dx ха X a. cos x b. In a • a* ✓ax C. sin x - ✓sin x d.…

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Q: For which x value(s) is the function f(x)=sin'(2x) defined and not differentiable? Check all that…

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Q: It is known that the range of the function f(x)= a sinx+1 for xER is -2<f(x)≤4, then a = ?

A: Given fx=asin x+1,     ∀x∈ℝ range of fx is -2≤fx≤4

Q: Find f'(÷) for f(x) = 2 sin z cos x

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Q: Let f '(x) = sinx - cos x. Where does the relative extremum value of occur? (a). 플 (b). (d). 프 (c).

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(T/4) = 5? %3D

A: Given: f(x)=cx+log(cos(x))  and f'π4=5 find values c

Q: Let f '(x) = sin x – cos x . Where does the relative extremum value of f occur? (a) 플 (b). 증 (0).플…

A: For relative extremum f'(x) = 0

Q: Q1. Differentiate the following functions with respect to x: i. y = x-% -4/x ii. y = x+Inx+ sin(3x)…

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Q: Which of the following functions listed below will result in differentiating f(r) = cosh(r) +e a…

A: Option A is correct.  If we differentiate for the first time we get f'(x) = sinhx - e^(-x)  Again…

Q: Differentiate the following functions with respect to X: i. y = x% - 4/x ii. y = x+Inx+sin(3x) iii.…

A: d/dx (x^n)=nx^(n-1) d/dx (sinx)=cosx  d/dx(cosx)=-sinx d/dx(f(x)g(x))=f(x)g'(x)+g(x)f'(x)

Q: Integrate the following functions with respect to x: (1–2x)(1+ x³) (i) y = x2 (ii) y = 1+°+ sec? x…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (c) Differentiate the following functions with respect to x. (i) х3 + 5y4 — 2 — 1. (ii) y = -…

A: Differentiate the given functions with respect to x.

Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: b) 5y = 2x? + sin (y) %3D

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Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

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Q: O Find the derivative of the g f X COsy = ya sinx followny %3D 4) (2x+3y)"= e" tany %3D () sin xty)…

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Q: dy Determine of the following function dx sinhx x+y= /1+ cosh x

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Q: If the derivative of y = etanx is y' = m etan x, what is m? A. sec x tan x B. 1+ tan?x C. 1- tan?x…

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Q: Evaluate the given function using homogeneous ydx = (x + Vy? – x² dy A. Arcsin (-) = In (A B.Arctan…

A: In this question we have to evaluate the given function using homogeneous.

Q: Provide an appropriate response. Find f(n) if f(t) dt x sin 8x.

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Q: Verify the formulas by differentiation.

A: To verify the formula ∫dxa2+x2=1atan-1xa+C using differentiation. We know that integration is…

Q: Let f(x) = In(cos(x)). For what value of c is f'l =CX + TC 1? 4. C =

A: We can solve it for the value of c as below

Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³; (4) y = x sinh 2x-cosh 2x (2) y =…

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Q: Evaluate f(x) dx, where f(x) = -TSx < 0 15 sin(x), 0< æ < r. T f(x) dæ =

A: Properties of integration ∫acf(x)dx=∫abf(x)dx+∫bcf(x)dx ∫sinx dx=-cosx+C ∫xndx=xn+1n+1+C

Q: Consider the function F (x) = 5 sin(t)dt dF and determine the derivative da 2xsin(x^2) cos(x^2) O No…

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Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³ (2)y=tan³ √/cot(7x); (4) y = x sinh…

A: Solution is given below:

Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: (d) y= Vrª +x² +1= %3D

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Q: Differentiate the function. y = tan[In(ax + b)] y' = %3D

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: )at a: is. sin acos e The deriva tive of a functian: y=logg

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Q: Differentiate the following functions: e2x+1x +2 .3 a) f (x) = sin (3x+2) %3D -1 sin(3x) V3t? +t-3…

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Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: dy Find dr using implicit differentiation. e*y = 4 O a. e ye O b. xe* С. -y O d. 1-y 1 O e. y 4.

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Q: Differentiate the following function. r(t) = (te ~!,5t In t,t sin t)

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Q: b) Differentiate the function y= sinx-xcos.rwith respect to x.

A: Given: y=sinx-x cosx

Q: For f(x) = In(sin(x)), find f'(x)? %3D

A: Given : f(x)=ln(sinx)

Q: Differentiate the function. F(t) = e6t sin(2t) F'(t) =

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Q: dy Find by implicit differentiation a. ペt=e4 b. Jxy=xy+| Sinx t 2 cos 2y=I %3D C-

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Q: Function y U dy du dy du dx dx y = sin(3x²) cos(3x²) _y = V5x² – 4

A: Given: The functions y=sin3x2cos3x2 y=5x2-43 To determine: The inner function u, outer function y,…

Q: 1. Differentiate the following functions: a. y = In(sinx) b. y = evx Vx2 – 1 coshV(x2 + 1) (10pts)…

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Q: (ii) (iii) x+ +sin y = x'y² %3D

A: The objective is to differentiate the given functions. (ii) Given y=x2+π This can be rewritten as,…

Q: The derivative of f(*) = sin(cos(cos())) is O f'(a) = cos(a) cos(sin(a)) cos(sin(sin())) %3D O f'(a)…

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Q: tan (3x)+y? = sinh(2y)+5x

A: Solution:

Q: Verify the formulas by differentiation.

A: Rule used: quotient rule.

Q: Find the equation of the tangent Ine at y= 0, given the inverse function x= (3y+ 2)(y+ 1) O y= 7x +2…

A: The solution are next step

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as…

Q: Find a function f such that ∇f = ex cos yi − ex sin yj + zk.

A: Given, ∇f = ex cos yi − ex sin yj + zk.