Compute the derivative ln(ex+1) / 2x+1

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 derivative of g(x)=integration3x2x (u2-1)/(u2+1) du

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Q: Using the Chain Rule, compute the first derivative of sin T-x.

A: We have given a composite function and we have to find derivative of function by using chain rule of…

Q: Shows the derivative function of: 2x² + ln x²(2x² + 5x − 1)

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Q: Find the derivative of f(x)=ln(x^3-x+2)

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Q: find the derivative of   ( -10 sin(x) ) / ( 5x ** 2 - 10 sin(x) )

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Q: 4. By implicit differentiation , find the 1st derivative of x3 + y3 + 6xy = 0

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Q: Sketch the x^2 And the derivative And integration

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Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: Derive the formula for the derivative with respect to x of csc x.

A: We will write cscx= 1/sinx  Then we will use the quotient rule to differentiate

Q: compute the derivative f (x) = ln(4x2 + 1)

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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: 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: What is the derivative of 2(x)ln(x)+x

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Q: Find the First Derivative:  v=csc 7x

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Q: f (x) = ln(x · 5*)

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Q: Find the derivatives of following fucntion (logx)tanx

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Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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Q: S(x)= Jx-5

A: given that f(x)=1x-5 find the derivative from first principle f'x=limh→0 fx+h-fxh

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

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

Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

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Q: Evaluate the 2nd derivative at the given point.

A: We differentiate both sides with respect to x. Then we plug the given point.

Q: Find the derivative: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

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Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )

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Q: Compute the derivative of ln r3 –1 V2x+5x²

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Q: Determine the derivative of 6x log3(x)

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

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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: x(2x+3) 17. f(x) =- (x° +1)

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Q: Find the derivative at the point (0,.5) x2+y2=(2x2+2y2-x

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Q: Find the derivative y=ln(2x^3+6x-1)^3

A: y=ln2x3+6x-13 take derivative y'=ddxln2x3+6x-13 y'=12x3+6x-13ddx2x3+6x-13

Q: 1. Use logarithmic differentiation to find first derivative of y = xsinx

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Using the Chain Rule, compute the first derivative of sin 1–x.

A: chain rule Let f(x) = g(h(x)) And let u = h(x) Using the above, function f may be written as: f(x) =…

Q: find the first derivative of the function. F(x)= (1+sin2x/1-sin2x)^3

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Q: Use logarithmic differentiation to find the derivative of the function. y - (cos(4x))"

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Q: ,2, (x²–1)* Dx (1+8x)5

A: To Determine: find the derivative using chain rule  Given: we have y=x2-141+8x5 Explanation: we have…

Q: What is the derivative of (ln(3x))/x^6?

A: Let y = (ln(3x))/x6.The derivative of y is with respect to x as follows.

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: Find the second derivative of 2x^2 ln (1/x^2)

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Q: What is the derivative of ln(sec(7x) + tan(7x))?

A: Let y = ln(sec(7x) + tan(7x)).Calculation:Obtain the derivatite of y as follows.

Q: Find the derivative of: ln(sin-1x)

A: We need to find the derivative of ln(sin-1x).

Q: Find the derivative using logarithmic differentiation. x(x + 4) (5x + 1)(3x +7) (Express numbers in…

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

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Q: 7. y= ln 2x³ 5х-3

A: Explanation of the answer is as follows

Q: flx)= -e, 1-x2 1-e

A: To find The derivative of f(x).