Find the directions in which f increases and decreases most rapidly at point P. Then find the derivatives of ƒ in these directions. f(x, y) = 3x² + 2xy+ 4y², P = (7, 8) Direction of fastest increase is Direction of fastest decrease is Derivative in the direction of fastest increase is Derivative in the direction of fastest decrease is

Q: Find the derivative of f(y) = 2 sin y + sin² y and then use it to find all coordinates on the graph…

A:

Q: Find the derivative of the function y=(ex−1)(ex+2) and calculate its value at x=0.

A: Differentiating with respect to x, we get

Q: Find the derivative of the function. 5x g(x) = [¨ cos(r}]dt cosx

A: We will use Lebnitz rule to differentiate the function .

Q: Find 3rd order derivative of y with respect to x , if x = a sint, y = b cost.

A: Given: x = a sint y = b cost -------------------------------------------------- To find: 3rd order…

Q: Find the derivative of the function. y = 9Vx y' = %3D

A: Our Aim is to find the derivative of y=9x -(i)

Q: Find derivative of the i function y = x*

A:

Q: Find the derivative of the function. y = 2e Vx %3D

A: Given y=2e√x

Q: find the derivative of y with respect to the appropriatevariable. y = √(s2 - 1) - sec-1 s

A:

Q: Find the derivative of f (y) = 9 tan (y) V 2 12 y³√√

A: To find the derivative of the below expression. fy=9tany−y2−12y3y

Q: Calculate the derivative of f (x) = cos (7æ³ + 2) %3D showing all your work.

A: Topic-derrivative

Q: ind the derivative of the y= ((2x) +3)

A: To find the derivative of, y=2x+3

Q: Find the derivative of the function y =2cosx – 3sin x +1

A: Given, y=2cosx-3sinx+1

Q: Find the derivative of the function f(x,y)=x2+xy+y2   at the point (-5,-4)in the direction in which…

A: Find the derivative of the function f(x,y)=x2+xy+y2   at the point (-5,-4)in the direction in which…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

A:

Q: Determine the derivative of the function defined by h(x,y) = Arctan (2) + V3Arcsin () at the point…

A:

Q: Find the derivative of the function. y = (tan-1(4x))2 y' = %3D

A:

Q: Find the slope of the curve y2 + x² = y* – 2x at (-2,1) Find the required derivative by applying the…

A: topic - slope of curve note - As per bartleby guidelines ,we are supposed to answer only first…

Q: find the derivative using the appropriate rule or combination of rules. y = (z + 1)4(2z − 1)3

A: The given function is y = (z + 1)4(2z − 1)3

Q: compute the derivative indicated. g(x, y, z) =x2 + y2 + z2, gxyz

A: Given function g(x, y, z) = x2 + y2 + z2

Q: Find the derivative of y given that coth-1 (21x³) y = 63x2 A 1–441x6 63x2 B 1–441x6 63x2 1+441x6…

A: Given y=coth-121x3

Q: Use implicit differentiation to find the derivative of: 9. х2 +x Arctany %3D у + 4…

A:

Q: Find the derivative of x2y? + x³ + y = 8 at (2,0). %3D Find the derivative of y = cot-2 (x).

A: 1) The given function is x2y2 + x3 + y = 8 and the point is (2, 0). Evaluate the derivative of the…

Q: Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1, 1) in the direction…

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Find the derivative of the function. y = 3 tan(x - V1 + x 1 + x2 y' = ||

A:

Q: е. Find the slope of the curve y 4.x arccos(r - 1) at the point (1, 2m)

A:

Q: Find the derivative of the function. y = xe¬x/ y' = %3D

A: ddxxe-x7

Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

Q: Find the derivative of y with respect to x. y= csc^-1 (x^2+1) , x>0

A: Given ,

Q: find the derivative of y with respect to the appropriate variable.13. y = 6 sinh x/3 14. y = 1/2…

A:

Q: The directional derivative of f=8x°y-2xy2+3z at point P(1,1,2) in the direction 2âx+2ây-âz is

A:

Q: Find the derivative of the function. 2x y = /3 cos(x) m cos(u") du y' =

A:

Q: find the derivative of y with respect to the appropriate variable.27. y = (1 - u)tanh-1 u 28. y =…

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

Q: Find the derivative of y with respect to z. y=5 (2)

A:

Q: Find the derivative of the xy+4x-(1/y) = 0.

A: →dxndx=n xn-1→duvdx=udvdx + vdudx

Q: Calculate the derivative of the function y(x) given by the equation x2+2xy+2y2=1 under condition…

A: For y=1 we find x

Q: Find the derivative of the function. y = 13 arctan V (v²) y' =

A: We have to find the derivative of the function  y = 13 arctanx.

Q: Find the derivative of the function. y = arctan 1 + x 1 - X y' =

A:

Q: At what point(s) does the curve y=; 3x – 4 have a derivative of -1? O 1) (2.0) 2) (-1,-7) 3)…

A: Given query is to find the value of x where seri is -1.

Q: calculate the derivative with respect to x.  y^4 -2y = 4x^3 +x

A: Given:  y4-2y=4x3+x To find: dydx

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: Find the derivative of the function f(x,y) = tan at the point (3, - 3) in the direction in which the…

A:

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

A: Definition used -       Leibniz's rule for finding derivative -…

Q: Find the derivative of y with respect to x. 26) y = sec-1|2x+3 5 26) y = sec

A: We find the derivative using the chain rule

Q: 2.) y = tan¬1 – 6•x³ y' =

A: We have to find the derivative of the function: y=tan-1-6·x3 We know the formula of derivatives,…

Q: Find the derivative of the function. f(z) 0.6z-0.4z2 - 0.8 f' (z) -

A:

Q: Find the derivative of the function. 7. y%3D Vx +2 y'

A:

Q: -2 In(x) Consider the function f(x, y) = 3y

A: We have to find the derivative of the function f(x,y) in the direction u=-5,2.…

Q: Find the derivative of the function f (x, y, z) = * ++ at the point (-8, 8,-8) in the direction in…

A: Given thta  f(x,y,z)=x/y+y/z+z/x  To find teh derivative of the function at point p in the direction…

Q: Find the derivative of the function. y = tan VX- X- 3 y' =

A: Given function is: y=tan-1x-3