directional derivative

Letf : R^2 -> R: (x,y) -> x^4 + y^2 + 2x^2y -1Answer the following:(a) Graph f(x, 0) against x in two dimensions and graph f(0, y) against y in two dimensions.(b) Draw the countour set f(x, y) = 3(c) Calculate the directional derivative of f at the point (1, 1) in the direction of thevector (−1, 1).(d) At the point (1, 1), find the direction of steepest ascent. That is, find the vector v∗ with length 1 that causes f to increase most rapidly.(e) Find the equation of the tangent plane at the point (1, 1) and comment on the relationship between the tangent plane and the slope of steepest ascent.

Find the directional derivative of f=xyz at (1,1,1) in the direction of 𝑖⃗ +𝑗⃗ +𝑘⃗

Example 3.4 Find the directional derivative of g(x, y) = ex2cos y at (1, π)in the direction −3i + 4j.

Consider the vectors u = (−3/5, −4/5), v = (4/√20, 2/√20), w = (−3/√11, 2/√11). For a functionf (x, y), the directional derivatives of f at some point (a, b) with respect to u and v are given by Duf (a, b) =14/5 and Dvf (a, b) = −22/√20. Determine the value of Dwf (a, b)

Find the directional derivative of V · (V f) at the point ( 1,-2, l) in the direction of normal to thesurface xy 2 z = 3x + z 2 , where f(x, y, z) = 2x 3 y2 z 4