Find a particular solution Yp of the given equation showing all steps including finding the complementary function (Yc) to make sure that it doesn't involve the e^(3x). y" + 16y = e^3x

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

Q: find y' for y = 2Vsinx sinh-1(logx). %3D

A: y'=log2· 2sinx-1.cosx.sinh-1(logx)sinx+2sinxxlog2x+1

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

A:

Q: cosh(3x²y) = ln(e*y + 1)

A: Differentiate the cosh3x2y=lnexy+1 with respect to x. dcosh3x2ydx=dln(exy+1)dx Use the chain rule…

Q: Find the first and second derivatives.  f(x) = ln(5x+1)  Please explain and show how to do this…

A:

Q: 1+ln(3x²) y = 1+ln(4x) ||

A: Given function - y = 1+ln3x21+ln4xDifferentiating on both sides with respect to x - dydx =…

Q: Differentiate y = /sin(x² + 3)cosx

A:

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: Find the First Derivative: y=log10(5x+3/5x-4)

A:

Q: Find Dxy for y = sinh-'(x5)

A:

Q: fx ln x dx.

A: According to the guidelines the first question can be solve in multiple question. Kindly repost…

Q: 2. f(x) = 3. g(x) = 5 In x – 2* 4. g(x) = 4x³ log, x

A: To find the derivative of the given function. 2). Given function is fx=x2ex. Quotient rule of…

Q: find nth derivative of y=x/(x+1)^4

A: To find the nth derivative of the function y=x(x+1)4=x+1-1(x+1)4=1(x+1)3-1(x+1)4

Q: kel derivative

A:

Q: Find the second derivative of 1/square root of 2t

A:

Q: 14. √ √2-√x dx

A:

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: ne side of a right triangle is known to be 150 cm long and the adjacent angle is measured as π/ 3…

A:

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: y у %3 4a/сosh a

A: Consider the given hyperbolic function y=4acosha The given function can be written as, y=4acosha=4a…

Q: Find dy/dx by implicit differentiation. 5 5 y3 dy/dx = (Express your answer using positive exponents…

A: We have given 5/x^3 + 5/y^3 = 1

Q: Calculate the derivative. 1 y = log 5x y' =0

A:

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: he measurement of the radius of the end of a log is found to be 20 inches, with a possible error…

A: Given that: Radius of log, r=20 inError in measuring radius, dr=18 in

Q: what is the derivative of this question with solution y= csc (4x² ) Arccsc (4x² )

A:

Q: One side of a right triangle is 150 m long and its adjacent angle is t/3 radians, with t/60 radians…

A: Use derivative

Q: 2. y=cot1-2x 3. y=log22x*

A:

Q: Solve the problem and give a detailed solution. Find the 3rd derivative of y = sin(ex)

A: y = sin(ex) Differentiate w.r.t.xy'=ddx( sin(ex) )y'=cos(x)ddx(ex )y'=cosexexDifferentiate again…

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: Integrate ∫(ln(x))/x

A: We need to integrate the given logarithm function:

Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

Q: Find and sketch an exponential equation of the form y = Ce^kx that passes through the points (0,8)…

A:

Q: Find the first derivative and solve for x. Complete solution please.

A: To find: The derivative of y=1+ln xx. Formula used: Quotient rule of derivative: ddxuv=v·u'-u·v'v2…

Q: 2x-x² a. 2 logz e e*10* c. e*10* + loge

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the first derivative in the form of dy/dx  y=(3x-2) sq rt(3x-2) please show all your work so…

A:

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Find the first derivative y= ln(3x)

A:

Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

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

A:

Q: Find the orthogonal trajectories of family of curves y = ax5 (SOLVE BY USING DIFFERENTIAL…

A:

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

A: Implicit differentiation

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: Given query is to give an example of exponential and logarithmic differentiation.

Q: 3x-4 Y = Arctan

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: Given,  The one side of a right triangle is 20 cm long and the opposite angle is measured as 30°,…

Q: Y = 2 Arccos ( 1 -) + v4x – x²

A:

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let d1, d2 be the diagnols of a parallelogram given,  d1+d2=18d1=2+d2 ⇒d1=10, d2=8 Area of the…

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A: