Calculate the derivative. f(x) = (9e* – 6x²) (x' + 1) (Use symbolic notation and fractions where needed.) f'(x) =

Q: Compute the derivative using derivative rules. y = sin(x2) cos(x2)

A: Given: y=sinx2cosx2

Q: Compute the derivative of the function y = 5 sin-'(x) at the point x = (Use symbolic notation and…

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Q: Find the derivative of the function. y = x°cos x - 10x sin x - 10 cos x

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Q: Find the derivative of f(x) = tan tan (3x2+2x)( Ans: (6x + 2) sec2 (3x2+2x) solution?

A: Let,

Q: Find the derivative of the function. 1-X y arctan, 1+x y'= I3D

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

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Q: Find the derivative of ƒ (x) = 5ª In (x).

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Q: 29. Find the 5th derivative ofy= sin2x

A: 29. Given function is, y=sin2x. The first derivative of y is, y'=ddxsin2x=cos2x·2=2cos2x   The…

Q: Compute the derivative using derivative rules. y = 4e -x + 7e -2x

A: Given:     To determine: derivative of the given function

Q: Compute the derivative of the function y = 7 sin¬'(x) at the point x = (Use symbolic notation and…

A: A detailed solution is given below

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 the second derivative and the points of inflection using the second derivative f(x) = ln(x) /…

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

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Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

Q: Find the derivative of ln(2x2)+ln(2x)+1/3 where x=1

A: Given,           The derivative of  ln2x2+ln2x+13 where x=1

Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

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: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Find the derivative of function. y = ln(5x3 - 2x)3/2

A: To find: The derivative of y=ln5x3-2x32. Formula used: Logarithmic power rule: ln ab=b·ln a Chain…

Q: Find the derivative of 1. y= tan (x* + 3x³)

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Q: derivative of f(x)= 3sin2x

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Q: sinx 3. f(x)=(x)*

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Q: Estimate the derivative of f(x) = sinx at x = π/6

A: Since,it is known that the derivative of the function with any variable measures the rate of change…

Q: Find the derivative of f(x)= (x^2)sinx

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Q: Find the 4th derivative of the function y=exsinx.

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

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Q: Compute the derivative of the function y = 6 cos- (7x) at the point x = (Use symbolic notation and…

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Q: FInd the derivative of f(x) =ln 1+ex/1-ex

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Q: find the derivative of y with respect to x. y= ln3x

A: We can solve the given problem using chain rule derivative.

Q: Find the derivative of ry = -3+x*y° using implicit differentiation.

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Q: Find the derivative 4 y = In x +

A: It is given that- y=lnx+4x To find the derivative of y, use the addition rule, i.e.,…

Q: The first derivative of the function y = 3x cannot be solved using implicit differentiation. Select…

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Q: Find the first and second derivative of f(x) = ln(x)/rootX

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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: 19. Find the derivative of 16 = xy using implicit differentiation.

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Q: Find the derivative of ƒ(z) = ln2x 1. 2z

A: We first expand using the addition property of log.

Q: Find the derivative of y = sinx / (1+cosx).

A: Topic  =Derivative

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

A: Apply exponent rule:

Q: Find the derivative of the function without using the Quotient Rule. y = -

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Q: Find the derivative of (ex + e-x )/(ex - e-x )

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Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

Q: calculate the derivative y = cosh−1(3x)

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Q: 3rd derivative of y sin 3x

A: Here we have to find the 3rd derivative of           y = -1/sin(3x)

Q: find the derivative of the fuction f(x)= 5sinx/3x+cosx

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Q: find the derivative of f(x)=sec(x^4)ln(9x-8)

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Q: Find the derivative of the function y using the increment method or three- step rule. vx +1

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Q: Find the derivative of y = arccos x + x 1-x²

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Q: Find the derivative of the function. Simplify wherepossible  x lnarctan x

A: Let f(x)=xlnarctanxDerivative formula:ddxlnx=1xddxtan-1x=11+x2arctanx=tan-1x