determine directional derivative f(x, y) = x²y³ – 4y on point (-1,2) on vector direction v = (2, 1). %3D Choose an option O a. -V5 а. -24 /5 O b. O c. V5 O d. 24/5 e. 5

Q: 3.) y = log2 – 6·x³

A: Explanation: Given that,  y=log2(-6x3)

Q: t2 sin wt

A: We have the formula  L{tnf(t)}=(-1)ndnFdsn(s), where F(s)= L{f(t)}

Q: Find the derivative of the function

A:

Q: f(x) = Arctan csc² ( 3x

A: Some derivative formulae: ddxtan-1x=11+x2ddxcscx=-cscx cotx Chain rule of derivative:…

Q: P= (3,2,;?)

A:

Q: Find the derivatives of the functions in Exercise

A: Given: r=21θ+θ We know that ddxxn=nxn-1                                                        ..1

Q: Find the derivatives of the functions in Exercise

A: The given function is u=5x+12x.

Q: 9x= (Jx+ x) (+xt) %3D

A: Given  g(x)=x+x2x3+x+2 To take derivative of g(x), we apply product rule (uv)'=u'v+v'u…

Q: Find the derivative of the function

A: The given function is, gx=x2+2x-1ex. The objective is to find the derivative of the function.

Q: Determine the anti derivative of the function.

A: Given Data: Function: fx=2x35+10x5-74x Similified the given function f(x).…

Q: b. f(x) = 3v2x %3D

A:

Q: f (x, y, z) = arctan(x² + 2y + z) At the point A(0,1,0) along the direction ñ, where n is the…

A: Given that f(x,y,z)=arctan(x2+2y+z)  For a function of three variables f(x,y,z), the directional…

Q: Determine the anti derivative of the function please

A: Here given function as fx=3ex+11-x2-2sec2x-71+x2

Q: a) x'+y = In xy x(t)3Darcsin VI+r' b) teR-(0} y(t)%3Darccos V1-1

A: (a) Consider the given equation. xy+yx=lnxy We have to find derivativedydxhere.…