Example 5.4.3.1 1. Find the maximum rate of change of f at the given point and the direction in which it occurs. f(s, t) = tet, (0, 2)

Q: ivative of p = 2xz nes maximum in t 3k

A:

Q: Find the first and second derivatives of the function. f(x) = f'(x) = f"(x) = Identify the intervals…

A: Given function, f(x)=x2+x2

Q: Find the first and second derivatives of the functions in Exercises

A: To find the first derivative, differentiate r with respect to θ, using the quotient, product and…

Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

A:

Q: et f and g denote differentiable functions. If f'(x) = g (x), then f(x) = g(x).

A:

Q: What is the partial derivative, ә ду [x²y³ - 2xy + x³y-2-2x]? 3

A:

Q: Find a function

A: This is very intresting question because there are so many function on an interval whose first…

Q: 77. er = 1+ x20 + 20 +...

A:

Q: Some values of a clifferentiable functionfand it derivative given belouw. are

A:

Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: Use the definition of the derivative to find f(x) where f(x)=DV3x+1

A: f(x)=3x+1

Q: 4 Determine the derivative of y = 3x

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Q6// Find the value of first and second derivative for the equation x² + xy - y² = y/x,at (1,1)

A:

Q: use product rule, find derivative of x.y³ 1.y³+x. 3y²y' 1.y³ + x. 3y² x. 3y²y' noe of the above

A: Let z=xy3

Q: Example: Find the directional derivative of f(x, y, z)=x²-yz+xz² at P(1,-4, 3) in the direction from…

A: Directional derivative of f(x,y,z) in direction of some vector a is given by , Directional…

Q: Find the critical points of the function. Then use the Second Derivative Test to classify the nature…

A: Critical points and classification

Q: b The curve with equation y = ax + passes through the point (2,0) - x2 where its gradient is found…

A:

Q: Find the directional derivative of the function at the point P in the direction of the point . f(x,…

A: