Differentiate. et y = 8x2 y' =

Q: Sinha Sechct) At

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Q: 11. y=3x+ ln x %3D

A: Topic - derivatives

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Q: Find Dxy for y = sinh-'(x5)

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Q: Find the derivative. y = 7x² – sinhx %3D

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Q: Differentiate  y=sin(ln(5x2-2x))

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Q: calculate the derivative. y = sinh(x2)

A: we have to find the derivative  y = sinh(x2)

Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: Use differentials to estimate the value. estimate =  exact value =

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Q: . Estimate dx with an error less than 10-3.

A: Series sum estimation:

Q: by implicit differentiation. dx Find - (5x + 2y)1/3 = x2 dx

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Q: Find the First Derivative:  v=csc 7x

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Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cmand height 12…

A: Given : Diameter of tin = 8 cm. Height of tin = 12 cm. Thickness of tin = 0.04 cm.   To estimate…

Q: Find the equilibria of the differential eq

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Q: he surface al derivative

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Q: y=C1x + C2e + x2

A: The givne equation is:y=C1x+C2e-x+x2To eliminate the arbitrary constant/s

Q: calculate the derivative y = tanh(ex )

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Q: calculate the derivative

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Q: Solve by Bernoulli ODE and Integrating Factor: y' = y2+ 3y cotx

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Q: calculate the derivative. y = sinh(9x)

A: First of all, consider the formula for the chain rule and the given function y. Then assume u and v…

Q: Find the y 'values and differentials for?

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Q: Evaluate: √ye dx By using Gamma function. is

A: I have given the answer in the next step. Hope you understand that

Q: The edges of a cube are found to be 10cm with an error ± 0.03cm The volume of the cube is then…

A: Let the side of the cube = s = 10 cmError in the side = ds = ±0.03 cmNow,Volume of the cube = V =…

Q: calculate the derivative. y = ln(coth x)

A: Given: y = ln cot hx To find: The derivative of the function.

Q: (1 point) Find dy/dx by implicit differentiation. x + y = 6 + x

A: Given: x+y=6+x2y2

Q: Integrate sec√x dx ÷ √x

A: We have to Integrate : ∫secxxdx Let x=t⇒12xdx=dt⇒dx=2xdt=2t dt Now, ∫secxxdx=∫sec tt(2t dt)=∫2 sec t…

Q: dx

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Solve by Integrating Factor: y' = 1+3y cotx

A: The solution is given as

Q: Find dyydx by implicit differentiation. 1 + x = sin(xy2)

A: In implicit differentiation we differentiate the terms in LHS and RHS and then re-arrange the terms…

Q: Find dy ldx by Tmplicit differentiation. tanLx-y)=

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Q: Integrate ∫(ln(x))/x

A: We need to integrate the given logarithm function:

Q: Find the derivative of the function. y = In(Icsc(7x)|) y'(x) =

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Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: Find the derivative. y = 7x ln(6x) dy dx

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Q: Integrate: dx

A: By substitution method, integration of function is solved step by step .

Q: 4 + sinh(3x) = 4 cosh(3x).

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Q: Give 1 problem application of differential

A: We have to explain a real life example of differential equation.

Q: Integrate: S dx

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Q: Calculate the derivative. y = ecoth (22x) (Use symbolic notation and fractions where needed.) dy dx

A: using chain rule

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Find y" by implicit differentiation. 5 + y = 6 5x

A: Please refer to the image below

Q: .Find an equation for the curve that passes through the labeled int.

A: We are aske dto find the equation of the curve.

Q: Differentiate the function. y=ln(x5sin2x)

A: Given function:

Q: 9 y = Arctan(+x, 1- 2x

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Q: The derivative of y=eSinh/x +cosh¬/x equals

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Q: Find the derivative car (x+y) = yrinx

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Q: (a) Sizl=1 dz.

A: Here we use property of analytic function.

Q: In( cosh(3x) - sinh(3x) )=

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Q: y=

A: