• If x = xf(y) – 1 then, 1. y' =1-fy) xf' (y) 2. y' = Lv)-1 xf' V) 3. y' =-f'0) xf(y) 4. y' = 1-f(y) f' (v)

Q: dx/dt = 2 and y=x^3, what is dy/dt when x=-4,2,6

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Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

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Q: A curve passes through the point (2,0) has gradient dy at point (x, y) that satisfy the dx equation…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 10yz²…

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Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

A: The given function is:z=18y2x

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

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Q: Solve for dy given xsin y - ycos x = 2 | dx sin y-ysin x А. cOS X-XCOs y sin y+ysin x В. coS X-XCOs…

A:

Q: 10

A: Given:

Q: dz at the point (1,1,1) if the equation 4xy +z°x-2yz = 3 defines z as a function of the two…

A:

Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

A:

Q: Find the value of 0z/0x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation is xy + z3x – 2yz = 0 and defines z as a function of the two independent…

Q: Find the value of dz at the point (1)1, If the equation 5xy+ z4x -Qy2 =4 %3| defines z as a function…

A: Given 5xy+z4x-2yz=4to determine dzdx  at  (1, 1, 1)

Q: Find partial derivatives of x3sin y + cos2x tan5y with respect to x and y

A: We have to find the partial derivatives of  x3siny+cos2xtan5y with respect to x and y.

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

A:

Q: what is the partial derivative of 2=Yytylnlxy

A: Given query is to find the partial derivatives.

Q: Find both first partial derivatives. z = exy

A: Given function is z=exy. Partial derivative of function means derivative of function with respect to…

Q: Find all the second partial derivatives. f(x, y) = ln(ax+by)

A:

Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: Compute the differential dy  for  y=(6x+sinx)^3

A:

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: Find both first partial derivatives. z = 4y²/x az ax az ду || ||

A: z=4y2x

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

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

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Q: Compute the differential dz of the function. 3,,10 x°Y %3| dz

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Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

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

Q: (3+y +2y² sin2x) dx + ex + 2xy -y rin 2x) dy=O

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Q: Find dy/dt at x = 1 and y = x^2 + 3 if dx/dt =

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Q: Find dx dt dx dt at x 2 if y= = - 2x² - 1 and dy dt = - 3.

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Q: Find both first partial derivatives. z = sinh(7x + 5y) az ax az ду || ||

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Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

Q: Find dy ax oy Impticit dipTErentation 3. Find 2nd derivative

A: 1) The given equation is 2x2+2y2=17 Differentiate both sides of given equation 2x2+2y2=17 with…

Q: Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial…

A: Given:       y=arctan3sinx4+5cosx First derivative:     dydx=ddxarctan3sinx4+5cosx…

Q: Find dx dt dx dt at x = = 2 if y= 2x² - 1 and dy dt - 3.

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Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

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Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

A:

Q: 5. Integrate: S (cose-sin8) de sec 20 6. Find f(3y – y³)ž(1 – y?)dy

A: 5. Given integral, ∫ecosθ-sinθ2sec2θ

Q: Find the mixed partial derivative at the point (2, 3) for h(x.y) = x sin(y) + y sin(x) + xy

A: The given function is, Differentiate the above expression with respect x partially.

Q: The Derivative az/ax of sin(xy+z)-sin(zx- * :y)+sin(yz+x)=1 is -ycos(xy+z)-zcos(zx-y)-cos(yz+x)…

A:

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.