f(x)=5x'+7x-1lx+3 f there is more than one zero

Q: 9. f √x³-1dx x

A: Given: I=∫x3-1xdx    ...1 As we know that; ∫11+x2dx=tan-1x+C

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: Find the general solution using Reduction of Order: y''=2lnx

A: Explanation of the answer is as follows

Q: 3x+4 3. f(x) = x2+3

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Q: Find derivative of 2x^4y^3-xy^2 using chain rule.

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Q: max value for y

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: 5. Find the first derivative of y = (2x³ – 1)5Vx² – 1 %3D

A:

Q: Q-3-Edaluate the fallowing Integration 1- X3 x21 2. 2- X+1

A: Use the partial fraction to solve the given problem.

Q: Solve by Chain Rule (V3x² + In(5X*)) y = tan

A: To differentiate the given function using chain rule.y=tan3x23+ln5x4

Q: f(x) = (6x² - 2x+1)^

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Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: By using the second derivative test for functions of two variables, find three positive numbers…

A:

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: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: x³tanh² (x*) sech²(x*) dx

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Q: An ant is standing at the point (1,1,3) on the surface of a bowl with equationz=x^2+…

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Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

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

A:

Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

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

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Q: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: 1.f(0) = (금x* + 3)" %3D

A:

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

A:

Q: How would you find the stationary points of partial derivative equations coming from a multivariate…

A: Stationary points:

Q: 3x+4 3. f(x) = x2+3 12 x3+6x2+3x 4. f(x) = 3x

A:

Q: Find anti derivative 3x^2(y^2+1)

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Q: Find the root between [-1,0] where f (x) = (x+2)' +2x – 5 with error epsilon=0.1 by using False…

A: There are many methods to find the roots of an equation in a given interval. One among such method…

Q: (2x + 3)4 (5x + 1)(x² + 3) y = (3х — 1)3, Find the derivative of the function x3 + 4 A. dy dx (2x+3)…

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Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

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Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: A curve passes through the point (2,5) and the gradient of the curve at any point is given by…

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Q: Find 2 at the point (4,1,6) for -6x² + 7 ln xz + 4yz² – 2e? = 0 %3D

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: Find the derivative of 5e* 1. y = e 6x 3. y = 2x+3x 2. y = e* + e3x 4. y = (e* + ex)1/2

A: Quotient Rule of differentiation : ddxuv=v.dudx-dvdx.uv2 deaxdx=aeax dxndx=n.xn-1

Q: 2. The derivative of y = (1 + Vx3) (x3 -2 V) is y'=-3x4-3xs-2z2-11xº.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = 1+8x - 3x2

A: i) The given function is fx=1+8x-3x2. Note that, the above polynomial function is real and defined…

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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

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Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

A:

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: What is the derivative of y (2æ)* O (2x)^(x) (1-2 In2x) O (2x)^(x) (1-In2x) O (2x)^(x) (1+2 In2x) O…

A: Given; y=(2x)x.

Q: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

A:

Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

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Q: When should I use partial integration and when should I use substitution?

A: When should I use partial integration and when should I use substitution.