find y' (a) by applying the Product Rule and(b) by multiplying the factors to produce a sum of simpler terms todifferentiate. y = (1 + x2)(x3/4 - x-3)

Q: Find the derivative of the following functions using the long method.(general process) Y=3+4x-x^2

A: This question is related to derivative. We will solve this problem by using basic defination of…

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Find the derivative of the function y = 2x sinh−1(2x) − √(1 + 4x2)

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Q: find the derivative:  y = ln (8x^3 – 2x) – 2x

A: According to the chain rule of differentiation if fx and gx is the differentiable function then,…

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

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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.

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Q: Find y" by implicit differentiation. x² + 4y² = 4

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

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Q: Find  y''  by implicit differentiation. 4x2 + y2 = 4

A: Given,  4x2+y2=y,we have to find y''Differentiate with respect to x,we get…

Q: Find y" by implicit differentiation. 3x3 + 4y3 = 2

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Q: 2sin x -1 2. y = cosx+ 2

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: Find the derivative of the functions. y=cosh^-1 (3x)

A: We have to find derivative of the function: y=cosh-13x Rewriting the function, y=cosh-13xcosh y=3x…

Q: find the second derivative and simplify the final result 9. xArctanx - ln (square root of x^2 + 1)…

A: y=x tan-1x-lnx2+1

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

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Q: fx て (X)

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Q: 8. Find the derivative of the function. y= In(1+x)

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Q: 9) Find the derivative of y = (4x + 3æ²) (6 – 3æ) Use two methods: Product Rule and Foil First…

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Q: (3x+4` x² +5, y = tan

A: We know that d(tanx)dx = sec2(x) Now we will apply chain rule , Here we have    y = tan3x+4x2 +…

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: In 2x y = - cos x

A: ddxln 2xcos x= ddxln 2x . cos x - ln 2x.ddxcos xcos2 x= 12x. 2. cos x - ln 2x.(-sin x)cos2x= cos xx…

Q: Find the derivative of the functron. Simplify and express the answer anly. using positive expenents…

A: In this question the given function is y=(x2-5)3x2+3 we have to find y' In positive exponents only

Q: 3x y = .3 х +3x

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Q: In(3x) Find the derivative with respect to x of y 3x

A: We will use the quotient rule of differentiation to find the derivative of y. Chain rule of…

Q: Find the derivative and simplify exy -x² = 4Y² %3D

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Q: by implicit differentiation if x² +9x+9xy-y² =16 Find x dy

A: Find dydx by implicit differentiation if x2+9x+9xy-y2=16. Solution: Power rule of differentiation…

Q: Find the derivative of the function y = cosh−1(3x)

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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 equation of the tangent line to the function f(x) = ln (7 – 4x) at x = 1. (Use symbolic…

A: Slope of the tangent is obtained by dy/dx

Q: 1. Y= 3x -x- 2

A: Find your answer below

Q: find the second derivative and simplify the final result. 3. 4ln(Arctan x) = 1-y

A: The given function is 4lntan-1x=1-y It can be written as  y=1-4lntan-1x Differentiating with respect…

Q: Solve using a derivative y= 2x tan (3X+1)}" 3. 2.

A: Consider  y=2x3tan3x+12

Q: Find yu by implicit differentiation: 4xi+ By° = 8 3.

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Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

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: What is the derivative of the function  x^8(ln(x)), and what can I substitute for x to make the…

A: We have to find derivative dy/dx and point where dy/dx =0y is given below:

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

A: Please refer to the image below

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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

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Q: Find y" by implicit differentiation. 3x" + 4y - 2

A: differentiate it with respect to x.

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

A:

Q: Find y'' by implicit differentiation. 5x2 + y2 = 4

A: Implicit differentiation

Q: Find y'' by implicit differentiation 4x3+3y3=6

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Q: Find the derivative of y = ex². (Use symbolic notation and fractions where needed.) ||

A: We have to find the derivative of y = e9x^2x

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: Find the equation of the tangent line to the function f(x) = ln (13 – 4x) at x = 1. (Use symbolic…

A: We have to find the equation of tangent of ffx=ln13-4x at x= 1 at point x = 1

Q: Find the derivative of the function. X +8x + 3 y3D VX

A: Here we use the quotient rule of differentiation ddxuv =vdudx-udvdxv2

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: 7. y= ln 2x³ 5х-3

A: Explanation of the answer is as follows