Differentiate: f(x)=ln(x5−5/x3) f'(x)=

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: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

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

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Q: 11. y=3x+ ln x %3D

A: Topic - derivatives

Q: Determine the first derivative of the ff. function dz y = e? sin x + In x (arcsin z) with dx 4

A: Determine the first derivative of the function                   y=ez sin x + ln x (arcsin z)  With…

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

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

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

Q: Differentiate  y=sin(ln(5x2-2x))

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Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

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 of the function  y'=ln(squared root of x^2-4) and  y=ln IsinxI

A: The given function is y=lnx2-4. Obtain the derivative as follows.…

Q: find derivative d/dx ln(3x/(2x+7)^1/2)

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Q: Find the anti-derivative: x2/3 dx. Upload Choose a File

A: Using simple integration method to solve the question.    Attached below is the detailed solution.

Q: 2. Use logarithmic differentiation to find first derivative of y (sinx)r

A: Formula used: ddx[u(x)v(x)]= u(x)v(x).ddx[ln(u(x)).v(x)] ddx(u.v) =dudx.v + udvdx

Q: 2. Use logarithmic differentiation to find first derivative of y = (sinx)*

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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. y = (ln x)2

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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 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: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

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Q: Find the derivative of  y=ln [tan-1(7x5)] with respect to x.

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Q: Integrate ∫(ln(x))/x

A: We need to integrate the given logarithm function:

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. f(x) = x6 ln(x)

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Q: x(2x+3) 17. f(x) =- (x° +1)

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Q: Find the derivative. y = 7x ln(6x) dy dx

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Q: Find the second derivative of the function. g(x) = √x + ex ln x

A: Consider the given function gx=x+ex lnx Now, differentiate the given function with respect to x…

Q: what is the derivative of f(x)=ln(tanhx)

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

A: Consider the following equation: y=exlnx Differentiate y with respect to x: dydx=ddxexlnx Apply the…

Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Find the derivative. y =(ln(ln x))3

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Q: Compute the derivative of (ln x)^ln x

A: To find the derivative of (ln x)ln x Using the exponent rule ab=eb ln a we get, (ln x)ln x=e(ln x)ln…

Q: Differentiate the function. y=ln(x5sin2x)

A: Given function:

Q: Find the first derivative y= ln(3x)

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Q: 4x dx

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Q: 4. y=ln(4x' +5)

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Q: 4.x³ (log3 x)° b. y = (csc5 x) /sinh(2x – 8)

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Q: What is the derivative of the function  x^8(ln(x))?

A: To find the derivative of the function x8(ln(x)) as follows.Redefine the function as follows.

Q: calculate the derivative y = sinh(ln x)

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Q: Use logarithmic differentiation to find the derivative of y with respect to the independent…

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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 y = 1/ln(1 − 7x)

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Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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Q: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10

Q: 3. Use logarithmic differentiation to find the derivative of the function. (2x – 1) Vx+1 y =

A: giveny=(2x2-1)5x+13taking log on both sidelogy=log(2x2-1)5x+13using log…

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

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Q: Find the derivative.  y = ln((x + 1)(2x + 9))

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Q: Find the derivative of f(x) = 3/x ln(x), f' (æ) =

A: Chufu