Find y' at the point (4, 4) where z sin(z² – y²) + 13 = 2² – 3.

Q: y=8sin(x)cos(x) ; x=pi/3

A:

Q: Find the partial derivative. z = sin(9x°y – 10xy²)

A: Given: z=sin9x3y-10xy2

Q: 6. Use parametric differentiation to find if x= 212 +2, y=t* -7 dx Solution:

A:

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

A:

Q: Find the differential of the function w=x^5sin⁡(y^5z^4) dw=  dx+  dy+  dz

A: Differential of a function is simply the derivative of a function. Also, d(uv) = u.dv + du.v

Q: (b) Find the equation of the tangent line to the curve 8x²y3 – 5x2 + 7y3 = 10(x – 3y), at the point…

A:

Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: Find the differential dy. y = 6x7 + 3x2

A: Given:y=6x7+3x2

Q: Determine the differential of the function y=x3−3x2+4x at the point x0=1 when dx=0,1.

A:

Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: Find the differential d5y of the function y=sin2x.

A: To Determine: Find the 5th differential of the given function y = sin(2x)

Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

A:

Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: If sin(5x - 5y + z) = 0, use implicit differentiation to find the first partial derivatives with…

A:

Q: Find fy ) for (x,y) Cos (x) sincy) exy

A: Given query is to find the partial derivative of the expression with respect to y.

Q: Let y tan(2x + 2). || Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: We have to find the differential dy

Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

A:

Q: Calculate the differential of the function y=2x x2−3 at the point x=3 when dx=−315.

A:

Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

Q: . z=tan 2x dx From their derivatives find

A: Question is solved.

Q: Find the derivatives of the functions y = sin-1√1 - u2, 0 < u < 1

A:

Q: y = sinx from x = = to x = n and the x axis 2

A: The required solution is:

Q: Find the differential of the function z=2x'y %3D

A: If z is a function of two variables defined by z=f(x,y) then the differential dz or total…

Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: Q) - Find of y = sin de dy ! -11

A: Siny = 1/x.

Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and dx = 0.3 Find the differential dy when…

A:

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

A:

Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: Let y = tan(2x +5). Find the differential dy when x 3 and dr = 0.1 Find the differential dy when z =…

A: Given that y=tan(2x+5) find the differential dy when x=3 and dx=0.1 find the differential dy when…

Q: find the differential dy if y= sqrt(2x^5-3x

A: Given query is to find the differential of the expression.

Q: dy Integrate dx = 4e®xand find equation of curve that passes through the point (1,7).

A: Given that, dydx = 4e8x

Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: Find partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

A:

Q: Find the differential dy when x = 3 and dx = 0.2 %3D

A: When you get function of function form to differentiate, we use the chain rule. y = f(g(x)) dy/dx =…

Q: 23-4z2-2一4 y = %3D 1+ Va

A:

Q: Find at the point (1,0) for cos xy + ye* = 0. dx

A:

Q: Find the differential of the function. y = V 4 + cos(0) -2 sin (0) dy V 4+ cos (0)

A:

Q: Find the differential of y=xsinπx2 at the point x=12 when dx=0,01.

A: We will use product rule and chain rule to find dy/dx

Q: Use differentiation rules to find y' = dy/dx.

A: Given,

Q: Find dy/dx by implicit differentiation. бх3 + x2у - хуз %3D9 y' = %3D

A:

Q: find the differential dy of the function y=x2sin(8x)

A: Find the differential dy of the function y = x2 sin(8x) as follows.

Q: Use differentiation rules to find y′=dy/dx   y = 3 · cos5 ( x − 4/x2 )

A: We apply the power rule then apply the chain rule

Q: 7 Find (b) x siny-ycosx-y = 1. dx

A:

Q: Find the partial derivative. z = sin (9x'y – 10æy?) dz

A: