Find y' at the point (6, 6) where x sin(x? – y²) + 33 = x? – 3.

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

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Q: Use implicit differentiation to find dydxdydx without first solving for y. x^4+y^4=−2 dy/dx=?

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Q: (1) x² + 3xy+y? = 4 (2) -=y² +1 x-y

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Q: Find the particular solution for: y' sin(2y) – cosx = 0, x =when y = 0 %3D

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Q: y = sin(x) at |0, 0, with four equally – spaced points

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Q: Find dy/dx of y = cos^-1(2x) * sin^-1(2x)

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Q: find dy/dx by implicit differentiation. 3cos(8x)sin(7y)=8

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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 dy/dx at x=0 if y= Cosu and y--3x

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Q: Find the first part ial derivatives of f (x, y) = 3y sin(x? +y?).

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Q: Find the length of the curve y=ln(sec(x)), 0≤x≤π/4.

A: please see the explanation below

Q: find dy/dx of y=cos2x-sin4x

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Q: Sx-3) (sin (In x) + cos (In x)} dx equals

A: Here we have to evaluate I=∫(x-3)sin-1lnx+cos-1lnxdx

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

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: 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: 16. ху : Vx2 + y?

A: Using implicit differentiation.

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

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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: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

A: Given: x2+y2=81

Q: Find the equation of the line tangent to the cardioid r = 1+ sin(0) at Ô0 =

A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

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Q: Calculate the derivative. y = cos 3x In (cos ²3x) y' =D %3D

A: We can find the derivative as below.

Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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

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Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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Q: Find the differential of the function y=xxe2x at the point x=1.

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Q: Find dy/dx by implicit differentiation. 3 cos (9r) sin (2y) = 8 dy/dx =

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Q: Find dy/dx by implicit differentiation. 6,,3 x°y - y = x dy/dx

A: On implicit differentiation we differentiate both sides of the equation with respect to x . Then we…

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: Find dy/dx by implicity differation.

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Q: 2. Find the length of the curve: y = 2 In (sin (÷x)); -< x

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Q: Find dy/dx by implicit differentiation. 19) x3 + y3 = 5 20) 2xy-y2=1

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Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

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

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

Q: dy Exc:" of y = tanh (x5 – 5x)² --

A: Solution:Given         y=tanh4(x5-5x)2  To find dydxFormula:ddx(xn)=nxn-1ddx(tanh x)=sech2x

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

A: Given that, dydx = 4e8x

Q: sin(2x) dx+cos(3y) dy=0,y(π/2)=π/3

A: Consider the provided differential equation with given initial condition,

Q: Find dy/dx by implicit differentiation. 4+6x=sin(xy^2) + y

A: Answer and explanation is given below..

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: 1I) (3y cos(3x)dx-sin(3x)dy)/ y 0

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

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

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Q: dy/dx of y=5^cos(3x+5)

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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: Find dy/dx of sin^2(3y)=x+y at (2 - pi)/4 , pi/4

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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: Find the length of the curve y = ln (sin x), π/6 ≤ x ≤ π/2

A: Given y = ln (sin x), π6≤x≤π2

Q: 4. cos x dy + y(sinx- 1) dx = 0; when x = n, y = -2

A: (4) To find: The solution of differential equation. Given: The differential equation is…

Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

A: