Discuss the relationsh ip between the derivative dy/dx and(lim) with drawing if it is required

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: Compute the derivative of the function y=arcsin1√x at x=2.

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Q: Find the equation of the tangent line to the graph of y at (2, 금). Use the limit process in finding…

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Q: Find the derivative of O2 sec 2x O 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

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Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: Compute the derivative ecos(x)arctan(x)

A: The given function ecosxarctanx.

Q: Use the Power Rule to compute the derivative: %3D lx=7

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Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

Q: Find the derivative y=arctan(square root 1+x/1-x)

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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: Compute the derivative of (arctan(x))^e^x

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Q: dy Discuss the relationship between the derivative and (Lim) with drawing if it is dx

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Q: =[in(4-x cos (r4

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Q: Show that the derivative of y- arccos (x) is ay- dx sing implicit differentahon an appropriakly…

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Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: use the general power rule or the shifting and scaling rule to compute the derivative  Y= cos4(ϴ+6)

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Q: Fin derivative of the funclions. y=Log

A: The given function is: y=log3xx-12

Q: Find the derivative of  arc csch tan(z)

A: Use the chain rule of derivative and simplify.

Q: Is it true that the derivative of y=arcsin(cos2x) is -2?

A: The function is y=arcsincos2x.   Differentiate the function with respect to x.…

Q: find the derivative of the function the limit process. by flx) %3D

A: Given f(x)=1x2We know that derivative of f(x) with respect to x is defined…

Q: Find the derivative of y = arccos 4x with respect to x.

A: Given that: y=arccos4x

Q: Find the derivative of y with respect to x. 1/9x²-1 + sec -13x, x> y= cot %3D

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Q: Find the derivative. Simplify where possible. h(x)  =In(Cosh  x)

A: Given: h(x)=lncosh x To find: we have to find the derivative of h(x)

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: Find the derivative of y(x) = In (8(In(x))'). (Use symbolic notation and fractions where needed.) dy…

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Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

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Q: Find the derivative of y = arc cot(3x)

A: Find derivative

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Find the derivative of y = arctan(x) by using implicit differentiation on x = tan(y).

A: Consider the provided function y=arctan(x).

Q: what the derivative fxy er hin ction Sas)=x'tan)

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Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: What are the indeterminate forms and L'hospital's rule in application of derivatives?

A: We have to define Indeterminate form and L'Hospital Rule

Q: Ay Find the derivative of the following using lim Ax-0 Ar %3D dx ala

A: Part (a) - y = 4x2-5x       ...........(1)Given that,dydx = limx→0 ∆y∆x We can write it as - dydx =…

Q: Find the derivative. Simplify where possible. y = x tanh-lx + In /1 – x²

A: We have to find

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Find the derivative. y = In(x²)tan (3x) %3D

A: Given:

Q: Find the derivative of the function. simply if possible y = arccos(e2x)

A: We have to find the derivative of the function: y=cos-1e2x We know the formula of derivatives,…

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

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Q: Find the derivative dydx of the lemniscate of Bernoulli given by the equationr2=cos2θ.

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Q: есх Find the derivative of y = Arccot (tan(esec*)) in its simplest form secr

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Q: fox)= x+ ?

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Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

Q: Calculate the derivative. y = In (tanh (5x)) (Express numbers in exact form. Use symbolic notation…

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Q: Find the fifth derivative using product rule y = sin3xcos4x Where r is the last digit of your…

A: The fifth derivative of the given function can be found by differentiating the given function five…

Q: 2. Calculate the derivative of y = arccos(e arcsin(x2)

A: Let u=arcacos(e^x) and v=arcsin(x^2), then y=u/v

Q: Compute the derivative of y= arctan(arcsin x)

A: To Determine:  Derivative of given function:

Q: s(w) = In( w - %3D

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Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Q: find the derivative of y with respect to the appropriatevariable. y = (csch θ)(1 - ln csch θ)

A: Given information: The function is y=cschθ(1-lncschθ). Calculation: Find the derivative of the…