Calculate the derivative of the function y=log2 x ln (2x) at x=1.

Q: Find the derivative of the function.   f(x) = x5 ln(x)   f'(x)=

A: We have to find the derivative of function: fx=x5lnx Here there are two function in multiplication…

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

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Q: 3.) y = log2 – 6·x³

A: Explanation: Given that,  y=log2(-6x3)

Q: What is the derivative of `y=\ln\ x`?

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Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: Find the derivative of the function f(x) = x√ln x

A: Here given Use the formula of product rule of derivatives as

Q: Find the derivative using the logarithmic y=ln (x+1)/x^2-2

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Q: Find the derivative of the function. y = x2 ln x

A: We use the product rule to find the derivative

Q: Find the derivative of function. y = log(2x)

A: A composite function is differentiated as follows: ddxfgx=f'gx·g'x

Q: Find the 3rd derivative of the function y=excosx.

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Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: Find the derivative, if y3 (log x)* + y = (log x)* +(sinx) -1

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Q: Compute the derivative in terms of log for y=log(xe^(-3x))

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Q: find the derivative of y with respect to the givenindependent variable. y = θ sin (log7 θ)

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Q: Find the derivative of the function. y = (ln x)4

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Q: Find the derivative of the function.

A: Given y=lnx+1x-1

Q: Find the derivative of y =log2x

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Q: Find the derivative of the function. y = ln√(x2 − 4)

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Q: Find the derivative of the function g(x) = log3 √(1 − x)

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Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: Find the derivative, if y = (log x)" +(sin x)™* -x %3D

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Q: y = (cos(x²))*

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Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: Calculate the derivative. 1 y = log 5x y' =0

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Q: use logarithmic differentiation to find the derivative of the function y=x^ln(6x) y'(x)=

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Q: Find the derivative of z=(ln5)e^x dz/dx=

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Q: Find the first derivative of = (ln x)* 4 y

A: From the given function; y=lnx4 We know that; The Power law: ddxxn=nxn-1 The chain rule:…

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: (d) y = xnz²

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Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: Find the derivative of the function. y = ln∣csc x∣

A: Given data:   The given expression of the given function is: .   Substitute u for csc x in the given…

Q: Find the derivative of the function. y= log 4- x

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Q: Calculate the derivative. 3 y = log 3X y' =D

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

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Q: x(2x+3) 17. f(x) =- (x° +1)

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Q: Calculate the derivative of the following function. y=2 log5 (x -3) 2 log5 (x-3) = (²-3) =] dx

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Q: Find the derivative using logarithmic differentiation. x(x+4) (5x + 1)(3x +7) y =

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Q: Find the derivative of the function. f(x) = ln(x2 + 3)

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Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

Q: find the derivative of y with respect to the givenindependent variable. y = log4 x + log4 x2

A: Given: By using logarithm base change rule, the function can be rewritten as follows,

Q: Find the derivative of the function: f(x)=ln[x^2÷(x+1)^3

A: Formula:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 5θ

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Q: f y = (sin x)x b

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Q: Find the derivative of the natural logarithm y=lnx.

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Q: Find the derivative of y= log, (5x³)+log, (sin.x)

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Q: Find the derivative using logarithmic differentiation  y= x(x2+1)/sqr root x+1

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Q: 2x+3) 17. f(x) =- (x² +1)*

A: topic - logarithmic differentiation

Q: Find the derivative of the logarithmic functions: y = ln ( 4x^3 - x^2 + 1^2)

A: Application of derivatives

Q: Find the derivative of the function. h(x) = log4(x + 9) h'(x) =

A: Topic = Derivative