Differentiate. 3 + 6x g(x) = 7 - 4x g'(x) = %3D

Q: 5. sech 2x tanh 2x dx

A: Consider the integral ∫sech2xtanh2xdx The objective is to integrate the function. Use the formula…

Q: 12. integrate (10x+6x +2x-6)dx

A:

Q: -3 S x(3x – 1)® dx

A:

Q: 3 4x Evaluate -dx. 4 2 x'-6 3 4x -dx = x* -6 4 (Round to the nearest thousandth.)

A:

Q: Differentiate  y = x ln x

A:

Q: Differentiate: y = x(ln x)² – 2x ln x + 2x

A: y=x(lnx)2-2x·lnx+2xy'=ddx(x)(lnx)2+xddx(lnx)2-ddx(2x)·lnx+2x·ddx(lnx)+2 , [product…

Q: 2x+ln(x) С. у %3 Vx

A:

Q: Integrate S(x-4)(x²-8x+12} dx

A:

Q: Differentiate   y = 3(ln x/x)

A:

Q: Differentiate   y = (ln x)2

A:

Q: 5. S(-5x-6 + 10x-11 – 20x-21)(x-5 –x-10 + x-20)dx

A:

Q: Calculates  ∫ln(x2+bx+c) note: 4c−b2<0.

A: Consider the given integral   Find the integration of first team,

Q: Differentiate   y = ln(x2 + 1)/(x2 + 1)

A: We have the given function as y=lnx2+1x2+1        ⋯⋯1 We know that, for two differentiable function…

Q: Differentiate   y = (x3 + 1) ln(x3 + 1)

A: Given, y=x3+1 lnx3+1

Q: Integrate S (2x+1) Staz+X+4) dx

A:

Q: Differentiate   y = 1/ln x

A: We can find the derivative of this function using the chain rule of differentiation (differentiation…

Q: Differentiate y = ln ( x 3 + 1 )

A:

Q: 7). S x² sech x³ dx

A:

Q: valuate (3x + 2)In(x) dx

A:

Q: (#10) S V4x2+9 dx x4

A:

Q: Evaluate. .3 S (-x² + 4x – 5)dx -2

A:

Q: Differentiate  y = (ln x)5

A: Given that the function is  y = (ln x)5 To differentiate with respect to x

Q: 2 1. x(-x² + 1) dx 16 dx 4x2 2. 3. dx x3/7 -V4x dx 4. 5. . (-2x! – x295) dx

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: 5. Lva – 2r dx 6. 5x+2

A:

Q: x3 e2x dx. Integrate

A: ∫12x3e2xdxThis can be done by two steps;Step-1:integrate without limitwe can integrate by parts∫fg'…

Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5)

A: Given,

Q: Differentiate.  y = ln[e2x(x3 + 1)(x4 + 5x)]

A: Solution: Consider the given equation: y = lne2xx3+1x4+5x We know that  log (m.n) = log m + log n…

Q: 3 d. S16 – 3x| dx 1

A: We have to solve given problem:

Q: 3 ln x + 2 ln y − 4 ln z

A: To simplify: 3lnx+2lny-4lnz Solution: 3lnx+2lny-4lnz On simplifying further we get:…

Q: 2 sec* dx

A:

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

A:

Q: Differentiate.  y = ln[(1 + x)2(2 + x)3(3 + x)4]

A: y = ln[(1 + x)2(2 + x)3(3 + x)4] y' = ?   We know: ln(AB) = ln(A) + ln(B) ln(A)n = n.ln(A)

Q: Integrate: S dx 5+ x2 5x

A:

Q: 4 4 + x2 Find 3 x° + + 4/x ) dx - -

A: Given integral, ∫x3+4x+4x2+4xdx

Q: Calculate S√4-x² dx

A:

Q: Shows : V9x² +25 (12) dx = 3 ln 3x + V9x² + 25 V9x² + 25 + C -

A:

Q: (#9) S x2 dx V16-x²

A:

Q: / solve: X Ln x dy + Xydx =Ln xdx

A: Solve by integration

Q: 2 の x3 ex lx の 2X dx to

A: 3 Given: ∫12x3ex dx   ……1

Q: How do you integrate: xe11x dx ?

A: Given integral

Q: tanh 2x ln (cosh 2x)dx

A: Evaluate the integral ∫tanh2xlncosh2xdx

Q: 6. S (2x+3) dx (x2+3x-6)9

A:

Q: x4 + Vtan y = x ln y

A:

Q: Evaluate ſ _dx V16-x 4-x

A:

Q: 6). S csch* 2x dx

A:

Q: 13) [[sech x – csch x }°dx

A:

Q: dy/dx of y=(fifth root of (6x-7))(ln(3x-2))

A:

Q: 5, S₂(4 - 2x)dx

A:

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: 4. S(5x +) dx = dx = 2 5. S- x7 x4- 15x6 6. S (四 극) dx %3D

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: