Logarithms with other bases can also be used as functions. We already saw that the derivative of log10(x) is 1 It turns out that the derivative of log, (x) is just So, for example, the derivative of x In(10) a In(b) 7 y = 7 log, (x) is y' x In(2) For the function f(x) = 3 log; (x): f'(x) = f'(7) =

Q: Using logarithmic differentiation fx) = x° [2x+ 3 (x*+1)4

A: NOTE: Refresh your page if you can't see any equations. . take log on both sides

Q: 3. (a) Use logarithmic differentiation to show why the derivative of a is a In a, where a is a real…

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Q: Using Leibniz find the third derivative of the following function y = e2= Inx

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Q: Find the first derivative of: y=-3/√2+x

A: Given : y=-32+x To find the first derivative of the given function.

Q: Use logarithmic differentiation to find the derivative of the function. y = (cos(8x))x

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Q: Logarithmic Differentiation of (ln x)^x^2

A: Given expression

Q: find the second derivative of the function. g(x) = e6x ln(x) g''(x) =

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Q: se logarithmic diferentiation te find the derivative of with respect bo the given independent…

A: Differentiation

Q: Use the formulas of Derivative of the Algebraic functions and Logarithmic functions in determining…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first three parts of…

Q: Use logarithmic differentiation to find the derivative of the function. y = x6 cos(x)

A: We have,

Q: Find the first derivative of y = ( ex – e –x ) /  (ex  + e –x ) and y = ln [ x  +  √ (x2  + 1) ]…

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Q: he following function: y=x/ln(x) the derivative is the following: y'=ln(x)-1/(ln(x))^2 which…

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Q: The derivative of the function y = log2(In(x)) is: 1 1 y': x In 2 In x y' = x In 3 ln x the above…

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Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: Use logarithmic differentiation to find the derivative of the function. y = square root of (x-5…

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Q: Find the derivative of the function. f(x) = ln(6x) f '(x) =

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Q: (2) Use logarithmic differentiation to find . Do NOT use the quotient rule here. e4x y = (x3 + 4)3…

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Q: 3. Use logarithmic differentiation to find the derivative of y = x"". (Your answer should be…

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Q: Find the derivative of the function. h(x) = log2(x2 + x)

A: Given function is : hx=log2x2+x To find the differentiation of a given function.

Q: (a) Use logarithmic differentiation to find the derivative of the function. y (In x)seca (b) Find an…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 12. Find the second derivative f"(x) of f(x) = 4xe* 13. Use Logarithmic Differentiation to find the…

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Q: Find the derivative of the function using the chain rule. y = log10(7x)

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Q: Find the derivative of the function. g(x) = ln(|x9 − x|)   g'(x)=

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Q: sin® x(3x + 1) (4хт — 5)°(2л + 3)10" Use logarithmic differentiation to find y' if y

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Q: Using properties for Logarithmic function, Only Simplify without differentiation the following…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),    (3,…

A: Given equation of curve y = ln(x2-3x+1)

Q: Note, derivative of a logarithmic function f(x) has three parts and is given here: f ' (x) = 1/ln…

A: We know that loga u(x) can be written as : logau(x) = (ln u(x)) / (ln a) = p(x)

Q: Find the derivative of the function.   f(x) = ln(x + 4)   f'(x)=

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Q: Find the second derivative of the function. g(x) = e6x ln(x)

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Q: Use logarithmic differentiation to find the derivative of the function. y = (cos(9x))x

A: given that y=(cos(9x))x we need to use logarithmic differentiation to find the derivative of the…

Q: find the logarithmic differentiation of y=(x4+2)e^-x

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Q: Use logarithmic differentiation to find the derivative of the function. y = (cos(6x))x y' =

A: Use log to differentiate

Q: (2x+5)³(52²-2x) 4. Use logarithmic differentiation to find the derivative of the function y = √2x+5

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Q: 5. Use logarithmic differentiation to find the derivative of the function. (x²+1)6 tan² x y = X3

A: Explanation of the answer is as follows

Q: Find the derivative of y with respect to x Y=5 ln (3 ln x)

A: Given, y=5 ln (3 ln x) We have to find derivative of y with respect to x.

Q: Using logarithmic differentiation, Show that y(x)=xa2xex2 has no stationary points other than x=0,…

A: Given function is yx=xa2xex2. We have to show that the given function yx has no stationary points…

Q: Find the derivative of f with respect to x of f(x)=ln x8.

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Q: Compute using logarithmic differentiation to find y' of y = log(x +(x^2-1)^1/2)

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Q: 7. * y = ln x X

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Q: y = (3x-2)/ (2x-1)1/2        Use the quotient rule y = [ x1/3 (x-5)1/5]/ (3x+7)9      Use…

A: 1. y = 3x−2/ 2x−11/2y=3x−22x−1 Differentiate with respect to x y'=3x−2'2x−1−3x−22x−1'2x−12…

Q: Use logarithmic differentiation to find the derivative of the function. y = x7 cos(x) Step 1 Using…

A: Here, the given function is: y=x7 cos x⇒ln y=7cos x ln x

Q: x* (x – 2)8 f(x) = (x2 + 8)7 Use logarithmic differentiation to determine the derivative. Your…

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Q: Find the derivative y = 2* log3 x xln3 2* log3 x + xln3 (In x) · In 2 In 3 + n 32 x-In 3 None of…

A: At firts apply base change formula for log3x. Base change formula is logba= logea/logeb. Then find…

Q: II. Determine the derivative of the ff. logarithmic functions 4. y = 8 log 6 7x² 5. y = - 5 log 7…

A: Use the chain rule of differentiation to derivate y. Chain rule is used which is as follows- (i)…

Q: Use logarithmic differentiation te find the derivative of {» with respect bo the given independent…

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Q: 3. Use logarithmic differentiation to find the derivative of y = x". (Your answer should be…

A: To differentiate the below equation using logarithmic differentiation. y=xx2

Q: æ² (x – 8)5 Let f(x) (æ² + 3)² Use logarithmic differentiation to determine the derivative. (2² +…

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Q: g differential equa

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Q: Find the derivative of y = log7 (2 -3x) .

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Q: Find the derivative of the function. f(x) = ln(4 − x6) f '(x) =

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.