Suppose that f(x) = 11x – 4 ln(x), x > 0.

Q: find y' for y = 2Vsinx sinh-1(logx). %3D

A: y'=log2· 2sinx-1.cosx.sinh-1(logx)sinx+2sinxxlog2x+1

Q: Differentiate the following function.   y = ex ln x

A:

Q: (14) Use log differentiation to find the derivative of the function. Y = (sin (7x))*

A: Here, the given function is: y=(sin(7x))x Taking logarithm on both sides, we have: ln y=ln(sin(7x))x…

Q: 70ot(*) e*dx e2x +1

A:

Q: Find y' for y = (2(x^2+1))/(x(sqrtx+1)) using logarithmic differentiation

A:

Q: Find F'(x) if F(x)= e^(-x^2) * x^(sin(x^3)) Use logarithmic differentiation

A: topic - logarithmic differentiation

Q: Evaluate the limit or derivative using properties of logarithms where x3 needed. dx x5+1

A:

Q: Find the first derivative:  y=log1o 5x+3/5x-4

A:

Q: 16. Use logarithmic differentiation to find y'. (a)= (x2 + 1)tan(=) (b) y = (sin (3z))VE

A:

Q: Find the derivative: y = x [ln(x) - 1] O ln(x) - 1 о O x ln(x) O In(x) O 1 + In(x)

A: Given y=x[lnx-1]To find dydx:

Q: Find Dx [(πx^4−2√x+√3) /(2x^2 - x)(3x−2)]. Not by using logarithmic differentiation.

A:

Q: Find the derivative of y with respect to the independent variable. x2 y =log 8 Sx+1 1 8x+1 O In8 x2…

A:

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: )=1/x. Using this, compute the

A:

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

A:

Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: Find the nth derivative of the function y=ln(ax+b).

A: Given function is Differentiating with respect to x repeatedly, we get In general,

Q: Differentiate  f(x)  = log 10  ( 2+ sinx )

A: Rewrite the given function as shown below: fx=log102+sinxfx=ln2+sinxln10        since logab=lnblna

Q: Differentiate the following function.   y = ln(ex2/x)

A:

Q: Evaluate the derivative. * d (log10 (x)) dx (In(10)) O Option 1

A: we have to find the derivative

Q: Derermine The FirST derivative of : 千irsT OF F) = x³ .16 V5メ-2 こSioN Expa usiNG Logalith mic Ex…

A:

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: (log a) dx 1+x²

A:

Q: What is the domain of ln |x| ?

A: Given: fx=lnx To determine: Domain of a given function.

Q: Find the derivative of y with respect to x. y=log(base)5 e^7x

A:

Q: Solve for x in the interval 0 < x < 2n. log (sin (x)) – log (cos (x)) = 0 a) x = 5,

A:

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

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

A:

Q: Find dx 1- y = log (Sin x )- Cot - Vx 3 2. y = log( vx) = tan(x - y) 3- x Sec -x = y? log (sec x) 4-…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the technique of log differentiation to find when y = (sin(x))In(x) %3D dx and then evaluate it…

A: Given that y=sinxlnx find dydx using log differentiation

Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

A:

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: 2. Use Logarithmic Differentiation to find dy/dx for y = 3 x(2x+5) (x²+1)²

A: Explanation of the answer is as follows

Q: Find dx by logarithnic differentiation. (3x-2)(x"+3)

A: d(logx)/dx = 1/x

Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: Where is the function sin (log (r2 + y²)) continuous?

A: Function = Sinlogx2+ y2

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 Where is the function increasing and decreasing in…

A:

Q: * limt (x-sinx)\ x+1 10 log x^2+3 O 0.5

A:

Q: 3. Use Log Rule to integrate. J6x-5 dx a. 6х-5 b. S- 1 dx x Inx

A:

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: ミr

A:

Q: differentiation

A:

Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

A:

Q: 24. Find the first order derivative with respect to x of the function u = log(x+ x .

A: The solution for the above question is as shown below.

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

A:

Q: 5. Find using logarithmie differentiation: dy y = [sin(x)}!m(=)

A: Find using logarithmic differentiation:   y = [sin(x)]^ln(x)

Q: Suppose x6 e-5y = In (xy). Find Y by implicit differentiation. dx

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.