f(x, y, z) = exyz, g(t) = (8t, 3t², t³) Vf = g' = (fog)'(1) =

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: a. What is the gradient at the point (4,0,1)?

A: Consider the given function fx,y,z=x2+y2+2z2+3.  The gradient of a function is given by,…

Q: Find the directional derivative of f(x, y, z) = xy + z³ at the point P = (3, -4, -3) in the…

A: Use the given information.

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A:

Q: Find the final amount of money in an account if $3,900$3,900 is deposited at 7%7% interest…

A:

Q: Consider the function f(t, p) 3 (pе' +1—р)". a. Find an expression for f(t, p) and evaluate that…

A: Given that:f(t, p)=(pet+1-p)n

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

A:

Q: Differentiate the function f(t) = t (11t+ 2). Answer f'(t) =

A:

Q: Let f(x) = x x+1 g'(x) = X . Calculate g'(x), where g(x) is the inverse of f(x).

A: Let f(x) = x/(x + 1)We have to calculate g'(x) , where g(x) is the inverse of f(x).

Q: d,e,f

A:

Q: Find f '(2), where f(t) = u(t) v(t), ū(2) = (1, 2, -1), u' (2) = (3,0, 4), and v(t) = (t, t², t³).

A:

Q: x²+4 Compute the derivative of the vector-valued function: r(t) = ln- x-5 i+ sin ² tj + (t² + 1)²k

A: Given vector valued function r(t)=lnx2+4x-5i+sin2tj+t2+12k The objective is to compute the…

Q: g(t) = V(1 – 3t)4 + t4

A: