Find the directional derivative of the function z(x, y) = e³tan(y) + (x + 1)²sin(2y) at the point P(0, 77/4) in the direction of vector a = i + j√3. Present your answer in the exact form (don't use a calculator).

Q: 8. Find directional derivative of function z = xey at point P(1,0) in the direction from pointP(1,0)…

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Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x 1.

A: You have posted multiple question. As per the instruction, we are answering the first one. If you…

Q: Use the technique of differentiation to find the derivatives of the follow- ing functions. (1) y =…

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Q: f(x) = x³ - 5ex + 7x Find the first 2 values of the derivative vector when the derivative of the…

A: Given: The function, fx=x3-5ex+7x.   To Find: The first 2 values of the derivative vector when the…

Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

A: Explanation:

Q: 1 The line / is tangent to the curve y=1-- , where x0, at the point where x = a. Show that the…

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Q: Find oy y'

A: We have to find

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function