et f (1) = e², f' (1) = 5e², g(1) = –3, and g' (1) = 1. Find h' (1), where %3D h (x) = 9 (x) arctan (In (ƒ (x))) Please enter your answer in decimal format with three significant digits after the decimal point.

Q: findthe differential dy of the given function. y= arctan(x − 2)

A: we have to find the differential dy of the given function. y= arctan(x − 2)

Q: A normal is drawn at a point P( x,y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A:

Q: Find the differential equation corresponding to y=a cos (logx) +b sin(logx) or y=A sin (logx)…

A:

Q: d sinh x) = cosh x dx

A: By using hyperbolic functions definition, sinhx =ex-e-x2   and coshx =ex+e-x2

Q: An integrating factor for the differential dy + my = e-m² is dx equation

A: Given differential equation is dydx + my = e-mx

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

A:

Q: arctan x Xe fel Xaresecx d

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

A:

Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: he population y(t) of a certain microorganism grows continuously and follows an expo uadrupling time…

A: In this question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: Evalualte! dx cosX x+ メ+ 1

A: Given:

Q: |- find the general Solestion of the differential eq ladich

A: Note : According to company guidelines we can solve only first question. So please post other…

Q: x'+z=et; x(0) = 1

A: Take z as constant

Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

A:

Q: Find the differential equation of the family of circles with fixed radius, r=a+b,and tangent to the…

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

Q: 1. Find dy/dx which x = -1 y = 1/x arc tan 1/x  2. Find dy/dx which x = 1/e y= arc tan (ln x)

A: 1. Find dy/dx which x = -1, y = 1/x arc tan 1/x  Differentiating y with respect to x.  Since y is a…

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: sinh (:) dz dy dx

A:

Q: Find dy/dx in terms of x and y if cos^2(9y)+sin^2(9y)=y+7 dy/dx=   implicit derivative problem.

A:

Q: Find the differential equation of the family of parabola with vertex and focus on the x-axis

A: The given question is related with parabola. We have to find the differential equation of the family…

Q: A nomal is drawn at a point P(x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: Equation of normal at the point P(x,y) to the curve is Y-y=-dxdy(X-x). ⇒X=x+ydydx Thus,…

Q: Find if y = e* In(sinh x) dx

A:

Q: Find dy if y = tanh-1(5x²) csch¬'(In x). dx

A: Given: y=tanh-1(5x2)csch-1(lnx)To find:dydx=

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

Q: An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce…

A:

Q: The differential equation dudx=5u+10  admits one equilbrium solution that is    asymptotically…

A: The given solution is  unstable whose plot is shown below.

Q: Find the Differential Equation of the family of circles with center on the line y = x, and passing…

A:

Q: 5. Find where y = In(cosh(2x)) + /sinh-1(2x) + tanh² (7x). dy dx

A:

Q: Compute dy/dx for the function. 5) y = In sinh 6x

A: topic- derivative of a function

Q: Find the differential equation of the families of curved where, parabolas with vertex on the X-axis…

A:

Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

A:

Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

A:

Q: 4. ox x cost at cost of 3 procuct nule J cost dt + cost at [sint] + x CSLX)ま(x) = Sin x - 0 + x cos…

A: To determine ddx∫0x3 x cos t dt.

Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

A:

Q: Differentiate the following function.   y=ln(x+1)+ln7 dy/dx=?

A:

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 3- Coshx dy +ly sinh x +e) dx

A: We have to find the solution of differential equation

Q: In the following problems, obtain the differential equations of the given families of curves whose…

A: Parabolas with vertex on the y-axis, with axis parallel to the x-axis, and with distance from the…

Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

A:

Q: Find the differential equation of the family of circles with fixed radius and tangent to the x axis.

A:

Q: find the differential equation of a family of parabolas with an axis parallel to the x-axis

A: We have to choose the correct answer from the given option according to the given condition

Q: (1) | cosx In (sin x) dx (2) [ xe -TX | хе dx x (3) x -16 dx

A: As per guidelines, we are supposed to solve only first two questions. Please repost other questions…