By using u=ln(3x) and dv=6x dx, find ∫ 6x ln(3x) dx. Be sure to include the argument of the logarithm in parentheses.

Q: Show that : log (1+ x) 1+x? dx = log 2 8

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Q: Given that log x -3 and log y = 5, find log Vy.

A: The given expression is logx2y35 and logx=3   and   logy=5

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

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Q: At what value(s) of x does ln (1 - x2) = x - 1?

A: We need to find the solution of the equation given by

Q: What is the derivative of e7 ** (4 x*+11)3 y = (16 x2+8 x-5)5 vith respect to x? Hint: Take the…

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Q: Find the following higher-order derivatives.

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

A: Let f(x) = ln x) and g(x) = e-x Let f(x) and g(x) be positive for x sufficiently large,  a) f(x)…

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

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Q: If ƒ(x) = (7x − 2)² · (8x² + 8)ª, find ƒ'(x) using logarithmic differentiation

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Q: Use the properties of the natural logarithms to simplify the following expressions sin 0 a) In sin e…

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Q: Using properties of logarithms, we can rewrite the equation as In(y) - In(x7 cos(x)), which is…

A: Consider the equation  ln(y)=ln(x7cos(x))

Q: Express the following logarithms in terms of ln 2 and ln 3

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Q: | 1-x² y = log10 2- 5x

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Q: 'x + 2 3. -dx x + 1

A: To integrate: ∫x+2x+1dx Solution: Evaluating the integral.…

Q: By using natural logarithm (ln), find dy/dx for this equation, 384=(x+2)3/4(y+3)1/3.

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Q: Which of the following functions grow faster than In x as xoo? Which grow at the same rate as In x?…

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

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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: log 10x dx

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Q: ( 3x+log; x dx = ? ||

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Q: f(x) = (a

A: Here, let y=f(x)=x3x3ex3 Taking natural log (ln) on both sides: ln y=lnx3x3ex3⇒ln y=lnx3x3+ln ex3⇒ln…

Q: y = log (4x°)

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

Q: Evaluate : |(log x)sin' x dx

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Q: Prove that : log 2 xp

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Q: If y = loge (2x + 1)'/2 ? and x = 1 y'will be equal to Select one: O a. 1.3

A: The given function is y=loge 2x+112. Obtain the derivative as follows. dydx=ddxloge 2x+112=ddx12loge…

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

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Q: 4 f (x) = 3 (In (9x² + 7(log5(+Vx*

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Q: e ecse with the and of logarcdtlmc dffenatiation /-

A: We have to find the differentiation of the given y

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

A: Derivative.

Q: Evaluate: dx (x+1) log(x+1)

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Q: A Disguised Form of the log Rule, Find

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Q: x-1 y = log XArctanx - Invx2 +1 = y x+1

A: We can find the second derivative as below

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: If f(x) = (3x – 5)* · (7x² + 7)*, find f'(x) using logarithmic differentiation.

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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 with respect to the independent variable: f(x)= log base 20 square root x

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Q: Given that log x=2.5 and log y = 4 , find the value of log (yx)

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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: ` log x dx

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

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

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Q: Find the derivative of Log(22³). 1/22 3/z 2/z

A: Given problem is  : ddzln2z3

Q: Find each derivative 1)f(x) = e*+&r+1 2) g(1) = In(?* – \H x*(x7–3)² . 3) y = In(2 Vx+10 ) [Hint…

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Q: When is ln x negative?

A: When is ln x negative?