x+y =(x+y-1)+. dx log (x+y)

Q: Solve x*+6r34y dx+ +3x=+y = (1 + logx)* dx²

A: Given differential equation, x4d4ydx4+6x3d3ydx3+9x2d2ydx2+3xdydx+y=1+logx2 This is a homogeneous…

Q: Find dx by first using algebraic properties of the natural logarithm (x+7)(x + 8)³ (x + 2)°(x + 3)°…

A:

Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

Q: 1. logx = 2 %3D 2.ln(x + 1) = 5

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Q: log(x³) dx

A: Consider the integral: ∫logx3xdx…

Q: Log(X^3Y^2Z^7)

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Q: Solve: x a + y = logxsin(logx). dx

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Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.

Q: 25łn²(x) log (x) dx

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Q: y = log( 2x'Vx² -1) 8.

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Q: log3(x) dx

A: Given integral is ∫ 3x2+log3xdx. Consider u= 3x2.

Q: X-y 19. If log 3 (logx + logy), show that x+y = 11r %3D

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Q: (x² + 1)? dy if y Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

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Q: dy/dx of log5(y2-y) + csc-1 (x/π) = -3y

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Q: Differentiate. y= 11* . log 7x dx (11*. log 7x) =O

A: Given that

Q: 'x + 2 3. -dx x + 1

A: To integrate: ∫x+2x+1dx Solution: Evaluating the integral.…

Q: Find ay dx 3. 4. 5. y = 2e³x5tanhx y = xln(5x-2) y = sec ¹(log 7x)

A: Given :y=2e3x5tanhx4. y=xln(5x-2)5.  y=sec-1log7x

Q: 1) x³+ 2x - 2y = x² logx + x dx3

A: Since you've asked multiple questions, as per the answering guidelines we are supposed to answer the…

Q: Find y by logarithmic differentiation. y=x²X A O y = 2 In x+2 2 In x-2B O y = x²* (2 In x+2) .C O y…

A: Use log to differentiate

Q: Determine y′(x) if y(x)=(4x^3+6)^sinx.  Enter an exact answer in terms of a natural logarithm.

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Q: $400 invested at 7% compounded continuously after aperiod of 3 years

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Q: ( 3x+log; x dx = ? ||

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Q: (x-3 x0t5)Y Sin(lgx) Sin(logx) %3D

A: Cauchy Euler second order differential equation Let us consider differential equation of the form:…

Q: Solve x +y= logx dx

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Q: Find dy/dx if y=log(-4x^2+2)

A: To find the dy/dx of the given function.

Q: write the logarithmic equations in exponential form.

A: Since, you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Express as a single logarithm 4 log, x² + 3 log, ) – log, x X 5

A:

Q: Find d/dx(2x) Type ln(x) for the natural logarithmic function.

A: Given query is to find the derivative of 2x.

Q: Find d/dx(2^x) Type ln(x) for the natural logarithmic function.

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Q: 1. y = e9z-5 2. y = 2x ln(x +2) 3. y = (2x – 5) log(3x² – 6æ)

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Q: 2 Solve (x²D² - xD + 4) y = x² sin (log x).

A: Given differential equation is x2D2−xD+4y=x2sinlogx. We have to find the general solution of the…

Q: y=10x log10 X differentiate?

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Q: y=x^logv5(x) dy/dx=?

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Q: Differentiate. y =9* . log 7x (g*. log 7×) • log 7× dx

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Q: How would you find y' if x^y=y^x using logarithmic differentiation and keeping the answer in terms…

A: Given equation:The given equation is xy = yx.

Q: log/ yx-y+3 1-4xt y 4X - log 3 4x ニ

A: Graph

Q: Differentiate. y = 12* • log 6x d x (12*- log ex) = D 6x) = [ %3D dx

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Q: Find the logistic differen tial equation dy =ky 1- dx

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Q: Differentiate. y = 10 log 3X %3D d dx (10*. log 3x) =D • log

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Q: 2. x log x +y = logx. dx

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Q: 4. y = log(x² – 7) 5. y = ln х+2 x-3 31

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Q: dy Example 1: Solve x- +y= logx dx

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Q: f (x) = ex ln(5x) - ex^3 +2 + log(e2x^2), find f '(3)

A: The given expression is f(x)=exln(5x)-ex3+2+log(e2x2).

Q: d Find (2"). Type In(x) for the natural logartihtm dx function.

A:

Q: d -log(z) = dz z O O 2- 1

A: We need to differentiate the function log(z) with respect to z. Differentiation is the process of…

Q: Find d/dx(4^x). Type ln(x) for the natural logarithm function.

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Q: Differentiate. y= log 7x dx log 7x=

A: y=log7xTo differentiate.

Q: 1+logx 2. =D1. %3D 1. 196 16. Solve for x, 5-log:

A: We have to solve for x .

Q: Find dy dx given (х* + 3x — 1)° /1 – 3x³ y , by using property of logarithms.

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Q: Differentiate : a. y=log2√x b. y= 2x^(3x) c. y = (x+1)^x

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.