If f(x)= tanh 1 et , then f'(x) is et 1- ex? 1 O 1- (e*)2 | et O 1-(e*)2 попе

Q: Find the derivative of y given that y= x In x to ex A None of the given choices 1-In x-x In x B ex…

A: We can find the answer as below.

Q: Find the critical points of the function f(x)=sin2x−cosx on the interval (0,2π).

A: For critical points, first find the derivative of the function and equate it to zero.

Q: If x+y divided by x-y= x^2+y^2 and dx/dt=12, then what is dy/dt when x=1 and y=0? show all work…

A: Given thatx+yx-y=x2+y2x+y=(x-y)(x2+y2)  [cross multiply]x+y=x3+xy2-x2y-y3

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

A:

Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: verify the statement by showing that the derivative of the rightside equals the integrand on the…

A: Given statement :

Q: Directon. tanx 6. Oy= (sinx) Fan a ANS: AN

A:

Q: Limit as x approaches 0 1-cos(x)/sin(x)

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Q: Find the fourth derivative of f (z) = 37 + In(z) – 164z. Enclose arguments of functions in…

A: To Determine: find the fourth derivative of the function .  Given: we have a function…

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

A:

Q: roblem 1: Compute the derivative of each function a. f(x) = [ e' sin(3t) dt b. g(x) = | e' sin(3t)…

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Q: d arctan (tanh x) dx Show that sech 2.x.

A:

Q: If f(x) = x cosh x + 5 sinh x then f'(x) =

A: Find the derivative

Q: x2 f (x) = t² sin(2t) dt 1

A:

Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

A:

Q: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

A:

Q: Find Taylor s Sen'ey fer ci) f() = Sin (x) about x= | f (x) = los (x) about f(x) = about x=1

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

Q: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

A: Critical points are the points where the derivative of the function is zero or undefined. Our…

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

A:

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

A:

Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: (A) Prove that: cosh x + sinh x = e*

A:

Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: Plot f (x) = ln x − 5 sin x on [0.1, 2] and approximate both the critical points and the extreme…

A:

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: у %3DIn(In sec x)

A:

Q: Estimate approximate derivative of f(x) = x2 at x = 1, for h = 0.2, 0.2, 0.05, 0.01 using first…

A: Given function is fx=x2. We have to estimate approximate derivative of the given function at x=1 for…

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

A:

Q: Find partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

A:

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy

A:

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

A:

Q: Find the fourth derivative of f (z) = 57 + In (z) – 109z. Enclose arguments of functions in…

A:

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Q: A curve y = /(x) have length of the curve from x 0 to x= n/2. dy Vcos(2x - 2) as its first…

A: