Find the dervative: ln(√x4+x2)

Q: Evaluate. Use a capital C for any constant. 3. dx 3x -

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Q: So 1 x²+7x+10 A. B. C. D. 3ln 2-ln 2 3 3ln 2+ln 2 3 3ln 2-ln 2 5 3ln 3-ln 2 3 dx

A: The given integral, ∫011x2+7x+10dx use the integral formula, ∫dxx=ln x+C

Q: If f(x) = 4ln(6x + 3 ln(x)),

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Q: So 1 x²+7x+10 dx

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Q: Differentiate. h(x) = In(xe-2*)

A: First simplify the given function using properties of lograthim than simply take the derivative.

Q: iate ſ In(x + v1 +x²)dx

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Q: 2 cosh x +losion2x = 5

A: I am attaching image so that you understand each and every step.

Q: f(x) = 9x - 4 ln(x), x>0.

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Q: Differentiate  f (x) = 1/ln(x4 + 5)

A: We have the given function as fx=1lnx4+5         ⋯⋯1 We know that, from the quotient rule of…

Q: Evaluate. (Use C for the constant of integration.) /x* - x³ + 64 x4 + 8x2 dx

A: Given,          ∫x6-x3+64x4+8x2dx

Q: fay = 3x Ln(x²1) 3x = 3Ln(x²-1) + 3× · 3x BLn (x²-) +

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Q: Evaluate the integral (4x -7/13 – 5x13)dx. „7/13 (4x -7/13 - 5x13)dx help (formulas) -

A: We first distribute the integration

Q: I'm a little confused, about how d/dx(ln4x) becomes 1/4x(4)

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Q: h(x)=ln(6x+4/x^5/3sinx), find h′(x).

A: Use logarithmic property then differentiate

Q: Evaluate: (7-j3)ln(cosh(2+j5))

A: Needed Formulae, coshx=e-x+ex2 lna/b=ln(a)-ln(b) ln(a×b)=ln(a)+ln(b) To solve, (7-3j)lncosh(2+j5)…

Q: f(x) = x2 cosh 3x -

A: Simply, I have used laplace transform formula.

Q: Find y' if y = ln(7x2 + 3y2)

A: The given function is:

Q: Suppose that f(x) dx = 2. Calculate (5f(x) + 4) dx-

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Q: 2dx x (3(ln x)2 + 12 In r – 15)

A: Indefinite Integration

Q: 1. f(x)= Jx + 8x– 24 |

A: As per Bartleby guideline, only the first question has been answered.  Please repost mentioning the…

Q: evaluate using the appropriate method or combination of methods.

A: Factor the denominator

Q: 4. Evaluate: - V16. dx 16 x2 -

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Q: 1x x2 SI x +1)dzdydx 00-y2

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Q: find the derivative.

A: We know that , if Then, by Second Fundamental theorem of calculus, we have

Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: An appropriate substitution for 2x dx is V4 – x2

A: The given integral is:∫2x4-x2dx

Q: What is the antiderivative of 9x^2 times (1 + x^3)^1/2 ?

A: The given expression is,

Q: Explain why ln x is positive for x > 1 and negative for 0 < x < 1.?

A: Plotting: y=lnx

Q: M. MN = NO=2x+2 MO = y+1 LN= 5x-4

A: The figure is a square. The two sides of the square are 12y+3  and  2x+2. It is known that all the…

Q: Evaluate. (4x + 5x²) dx -2x dx 8. 9. dx 10. -5 for x 2

A: To evaluate: ∫-12(4x+5x2)dx Solution: We know, ∫xn=xn+1n+1+C    ..(1) Here, ∫-12(4x+5x2)dx On…

Q: Find the antiderivative of 2x((ln(10x))2

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Q: compute the higher derivative

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Q: f F(x)= 8x^2 ln(6x) Than, F'''''(x)=

A: Given that F(x)=8x2ln6x find F’’’’’(x)

Q: Differentiate the following e2x+3y = x2 - ln (xy3)

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Q: b. Find S 5x*(x5 – 1)dx using a suitable substitution.

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Q: Find the inverse of y = ln(x2 - 2) for x > ,/2.

A: Given function is y=lnx2-2. To find the inverse  of function. Replace both x and y with each other.…

Q: What is q′(x) when q(x)=ln((x^2+1)(x^3+x^2+2))?

A: We first separate the log using the product rule of log.…

Q: Compute dx. x2 + 4x + 8

A: Our Aim is to compute the integral given below:-∫02 xx2+4x+8dx -(i)

Q: Integrate the function. dx x > 8 x2x2 - 64

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Q: Evaluate and simplify. L dx 1 V1-2x-x²

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Q: 1. S Vx4 – 10x3 + 25x² dx -

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

Q: Find the antiderivative of... f(x) = 5x - (square root)x

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Q: / log, (x2) dx

A: According to the definition of the logarithm, if y=ax, then logay=x. The logarithm with base e is…

Q: 三 直 Find hp x2² (2 ln (x) – 2) O1² 2x(x)2x-1 2 In (x) +2 In(x)x²= x2 (2 ln (x) + 2) +66

A: The solution are next step

Q: 413 xdx X csc 2. (sec2/3 xcsc4/3

A:

Q: how does ln(e1/2*e7/5) = 19/10?

A: Given expression is  We know that (x^m)*(x^n)=x^(m+n), so we have

Q: Differentiate y=ln [4x(x−7)/(x^3)]

A: Given function, y=ln4xx-7x3 It can be written as y=ln4x-7x2y=ln4x-28x2

Q: Find the antiderivative of ln(x)/x7

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Q: Find if y=tanVx³). dx 1 A 1+x³ 1 (в 2/x³ (1+ x³) 3x2 (1 + x³) D 2(1+ x³)

A: Given query is to find the derivative of the expression.

Q: What is s′(x) when s(x)=ln(5x 3+2x 2+4x+6)?

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: