5. Consider the function f(r, y) = sin(x² + y²). (a) direction of (4,3). Find the derivative of f(r, y) at the point P(-/2,0, sin(2)) in the

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

A:

Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

A:

Q: 6. Find the equation of the tangent line to x² + 3xy + y² = 5 at the point (1, –4).

A: Given x2+3xy+y2=5       (1,-4)

Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

A:

Q: Find the tangent line to y = x -x+7 at x = 7. ,2 The tangent line to y = Vx -x + 7 at x = 7 is y =

A: We have to find tangent line

Q: 2. Find the equation of the tangent line to the curve y = x² – 2x - 3 that is parallel to the line x…

A: Given: The tangent line to the curve y=x2-2x-3 is parallel to the line x+y=1. To Find: The equation…

Q: 2. Find the equation of the tangent line to the curve y = In(x'-7) at (2,0).

A: Given :          y=lnx3-7

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: Find the equation of the tangent line to y = = at x = 1. y - V2 = - V7 (x - 1) A) E (x - 1) -- x y -…

A: The solution is given as

Q: 2 Find the equation of the tangent line to the curve y =xNx +5 at the point (2,6)

A:

Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

A:

Q: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

A: The objective is to find the equation of the tangent line.

Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Suppose that f(x, y) the point (x, y) = (2, – 6) is = xy. The directional derivative of f(x, y) in…

A:

Q: Find the derivative of y with respect to x. y = sec -1 (3x2 + 1), X>0

A:

Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* - ey + 4tg(y)

A:

Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3.

A:

Q: 3) Find the equation of the tangent line to the curve 6y³ – xy² + cos (xy) = 7 - at the point (…

A:

Q: Find the equation of tangent and normal lines to the curve xs sin(2y) = y cos(2x) at the ㅠ ㅠ point…

A: Solution of this question is

Q: Find the slope of the tangent line to the curve 2 sin(z) + 5 cos(y) – 4 sin(z) cos(y) + z = 7m at…

A:

Q: Find the point of intersection of the tangent line to y=sin 2x) at y=0 and the line x+2y=5-

A: Given: y=sin(2x)  and y=0       substituting y=0 in y=sin(2x)then    0=sin(2x)         2x=0…

Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Find the derivative of y with respect to x if y=∫0ln(3x) sin(6et )dt

A:

Q: 5. Find the equation of the tangent plane of sin(xyz) = x + 2 y + 3z at the point (2, -1, 0).

A: We have given the surface X,Y,Z at the point (2,-1,0). We have to find the equation of the tangent…

Q: Find the derivative of the function. y = (( 1- cos 2x ) /( 1+ cos 2x ))4

A:

Q: 1) Find the equation of the tangent line to the curve: x* + xy – y = 7 at (3,2) %3D

A:

Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

A:

Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

A:

Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

A:

Q: What is the value of the first order derivative of the closed function given as…

A:

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

A:

Q: Find the derivative of the function

A:

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

A:

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

A:

Q: Find the slope of the tangent line to the curve 2 sin(z) +4cos(y) –- 3 sin(z) cos(y) + z = 7x at the…

A: The objective is to find the slope of tangent line to the curve at the point (7π, 3π/2).

Q: Use the rules of differentiation to find the derivative of the function y= 3+6sin: a. y' = 3+6cosx…

A: To find the derivative of the below function. y=3+6sinx

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: 5. What is the value of the second-order derivative of the function with parametric expression x =…

A:

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Find the equation of the tangent line to the curve 2y³ – xy² + cos (xy) = 3 at the point ( 0,1) .

A: Given curve is:  2y3-xy2+cos(xy) = 3 For slope of the tangent, differentiate the curve equation

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Given: y=∫x22x2lnt dt

Q: What is the derivative of y = (sin (3x?)2? dy dr 12z sin' (3교2) VI-974 dy dr 12z sin (3z²) VI-9z4 dy…

A:

Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

A:

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

A: