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Q: Find the first derivative of y=x arcsin x + √1-x²

A: y=x arcsinx+1-x2

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 First Derivative: y=log10(5x+3/5x-4)

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Q: e point at

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Q: Differentiate  y=sin(ln(5x2-2x))

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Q: Differentiate y =( logx) sinx

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Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Given: y=cos4θ

Q: What is the derivative of the natural logarithm function ln x? How does the domain of the derivative…

A: Given: fx=ln x To find: (a) The derivative of f(x)  (b) Compare the domain of the derivative with…

Q: Evaluate the derivative: y = log2(log2x)

A: It is given that,

Q: Find the derivative of function. y = log2(2x2 - x)5/2

A: Given, y = log2(2x2 - x)5/2 To Find the derivative of function.

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

A: aur objective is to find the derivative.

Q: 5. f(x)=3x*e*

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Q: 1 ソ= 1- x

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Q: Use logarithmic differentiation to evaluate y'. y = (8x)ln8x

A: Differentiation: - Differentiation is the ratio of a slight change in one quantity to a little…

Q: (x) = ,2x+1

A: Explanation and solutions is given below....

Q: Find the derivative: ln ((x+1)/(2x-1))^(2)

A: First simplify the expression using properties of lograthim than take derivative.

Q: Differentiate the following function.   y = ln(3x+1) - ln 3

A: We need to differentiate the following function.   y = ln(3x+1) - ln 3

Q: State the derivative rule for the logarithmic function ƒ(x) = logb x.How does it differ from the…

A: Given: fx=logbx for finding derivative of given function, first we convert it's base in e then…

Q: What are the domain and range of ln x?

A: Given: y=lnx we know that in lnx, x>0 so, domain of given function is x>0

Q: x (2x+3) f(x) = (x² +1)*

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Q: compute the derivative g(x) = tan−1(ln x)

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Q: Find the derivative: y=ln(x200e4ln(x^2)-4ln(x)+3)

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Using chain rule to compute the derivative for y, consider the solution below.   First of all,…

Q: compute the derivative f (x) = ln(csc−1 x)

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Q: Calculate the derivative and use logarithm rules to simplify   g(x) = ln((x^3 + 2x)(x+1)^10)

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Q: y = csc 4x

A: Given function is y=csc4x. We know that, ddxfgx=f'gx·g'x And ddxcscx=-cscx cotx Differentiating the…

Q: Find the derivative of the function y = log3(x2 − 3x)

A: Consider the following: y=log3x2−3xDifferentiate w.r.t.…

Q: Use log differentiation. y = (cosx)lnx

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Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

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Q: X In Зх +1 y y' X

A: Given ; ln(x2/(3x+1))=y/x.

Q: Find the derivatives of function (log x)tanx

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Q: Use Gamma Function to evaluate dx

A: The definition of gamma function states that, Γn=∫0∞tn-1e-tdt where Γn=n-1! and Γ12=π. The given…

Q: Find dx by logarithnic differentiation. (3x-2)(x"+3)

A: d(logx)/dx = 1/x

Q: Find y" by implicit differentiation. 5 + y = 6 5x

A: Please refer to the image below

Q: y = csc-1 VE

A: We can find the derivative as below

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

A: Given function:

Q: 6x = 4

A: Simple differentiation problem...

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

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Q: Find the derivative of the logarithmic function. y = In Isec x + tan x|

A: We have to find the derivative

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

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Q: Calculate the derivative. y = cosh(x³)

A: We have to find the derivative of hyperbolic function.

Q: Find the derivative of f(x) Give answer in exponential notation with positive exponents

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Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

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

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Q: Find the derivatives of 20" log(tan x)

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Q: Find the derivatives of x log x.log(logx)

A: We have to find the derivative of-  x logx.log(logx)

Q: y = Arcsin (e2x)

A: