d (a) Find log, e". dx d. [log, e"] = d.x

Q: dy (x² + 1)? if y = 2) Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A: Here we have to find the the derivative of y

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: Find dx by first using algebraic properties of the natural logarithm (x+7)(x + 8)³ (x + 2)°(x + 3)°…

A:

Q: Find the integral: log7 X dx = %3D

A: Solve the following integral

Q: dy et y = (x³ – 18x)m(=). Find using the method of logarithmic dx - ifferentiation. Express your…

A: Topic:- derivatives

Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.

Q: How is the logarithmic function y = log a x defined?

A: To define the given logarithmic function.

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

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Q: X-y 19. If log 3 (logx + logy), show that x+y = 11r %3D

A:

Q: (x² + 1)? dy if y Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A:

Q: Differentiate g (†) = 4 log, ( t ) – In ( t )

A: Given g(t)= 4log3(t)-ln(t) Now we have to differentiate g(t) as shown below

Q: ind the derivative of the given exponential and logarithmic functions. 11. y = e-2x²+1 12. A(x) =…

A:

Q: d Find (3"). Type In(x) for the natural logarithmic dx function.

A: we have to find the derivative of 3x

Q: dy Use the properties of logarithms to help perform dx COs x y = ln 3 – 5x2 - dy dx ||

A: As we know that ddxlnx=1x

Q: | 1-x² y = log10 2- 5x

A:

Q: Determine y′(x) if y(x)=(4x^3+6)^sinx.  Enter an exact answer in terms of a natural logarithm.

A:

Q: If logy =c- log,x, where y> 0 andx > 0, then y is equal to A. c-X В. 3 D. C.

A: To solve the given logarithm

Q: at any point h (1, 1) is logx – x

A:

Q: Express log x Vy/z in terms of logarithms of x, y, and z.

A: Express log x4y2/z3 in terms of logarithms of x, y and z.

Q: Express the guven auantity In (xt2)" single logarithm. ' + I LIn x-In (x? + 3x +a)°J as a

A:

Q: S (log æ + – 5x) dx =?

A:

Q: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?

A: What happens to the rate of change of the logarithmic function y = loga x as a becomes larger?…

Q: dx Evaluate log - 1+ax 1-ах

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Q: Find d/dx(2^x) Type ln(x) for the natural logarithmic function.

A:

Q: Find the function of the form y log,(x) whose graph is given.

A: Given that: Graph of f(x)

Q: y=10x log10 X differentiate?

A:

Q: y=x^logv5(x) dy/dx=?

A:

Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

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Q: find the deliva tiva dy for the function by using logarithmic

A: Derivative.

Q: Differentiate. y =9* . log 7x (g*. log 7×) • log 7× dx

A:

Q: log log (y) = A * e ^ x + B * e ^ (- x)

A:

Q: y = log, x %3D 1 1 1 2 4 8. 16 8 4 2 y.

A: given y=log2x complete the table x 116 18 14 12 1 2 4 8 y

Q: = log z in the regio

A:

Q: Sind dx/dy if ys log Vitx? 14

A: Given: y=logx1+x2+logx1-x214. So,         dydx=ddxlogx1+x2+logx1-x214…

Q: If y = loge(sin x)? dx will be equal to dy

A: Given: y=logesinx. To find: dxdy Solution: Chain rule of differentiation states that:…

Q: d -log(z) = dz (Z

A:

Q: Find Y for the following function: dx 3- y = log,(x3- x) 4- y = In 5- tan-1 V4x – 5

A: we have to find the derivative of the following

Q: Differentiate the function T(z) = 2z log2 z.

A: The given function is,

Q: question b

A:

Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

Q: d 1 -(log, (x))= dx x > 0 x In a

A:

Q: dx Express your answer in logarithmic form. x2 + ax

A: ∫dxx2+ax

Q: Find Log (x In x) Log (x Log x ) dx if

A:

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = logy x

A: Given that: fx,y=logyx To calculate δƒ/δx Partial derivate the given function with respect to “x”…

Q: Vx²-1•sin x y%3= %3D (2x+3)4

A: To find: The derivative of y=x2-1·sinx2x+34 using logarithmic function. Formula used: The derivative…

Q: Rearrange this equation to isolate A. H = K + log A =

A: Here I am attaching image so that you understand each and every step.

Q: Express th equation in exponential form.

A: (a) Given expression is log35=x. Express the above equation in exponential. logab=c, then…

Q: Find d/dx(4^x). Type ln(x) for the natural logarithm function.

A:

Q: d log, x = 1 dx [(In a)(x)]

A: