Q. Find the rate of change of z = In Vx² + y² at (3, 4, In 5), (a) In the direction of the positive x-axis. (b) In the direction of the positive y-axis.

Q: 3y > » √+x4 Definc f(x,y) (a) Find the rate of change of f at the point (-1,1) along the direction…

A: Given: fx,y=3y1+x4 To find: (a) Rate of change of f at the point (-1, 1) along the direction <1,…

Q: The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 97/(6 + x² + y2),…

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Q: Find the maximum rate of change of the function f(x, y) = 5y5 at the point (2,4) (Round the answer…

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Q: Find the directional derivative of the function f(r, y) = xy +x?y? - 2y at the point Po = (2, 1) in…

A: Find the directional derivative of the function at  point.

Q: Find the gradient of y = e" at the point (1, e).

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: dy If y2=2x+3y dx find then use it to find the tangent line to the curve at the point (3,2) For the…

A: Solution is given below:

Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at the…

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Q: Find f'cx?, f"cxx) wheve fcK) = xe -2 Jc %3D

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Q: What is the gradient of the tangent line to the curve y = 2x³ – 3x2 at the point with a = 2? |…

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Q: Find the equation of the tangent plane to f(x, y) = x² - 2xy + 5y2 having slope 2 in the positive x…

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Q: What is the derivative of f(x,y) y° at P = (3, 1) in the direction toward %3D Q = (4, –3)?

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Q: What is the gradient of the normal to the curve  y=x3  at the point when x = 1/2 ?

A: The curve is y = x3.   So, gradient of the tangent at any point (x, y) on the curve is…

Q: Find the magnitude of the greatest rate of change of f(x, y, z) = (x2 + z2)3 at (1, 3, -2), and…

A: Consider the provided question,

Q: f(x.y) = x³y – . Calculate Se af and əx ду

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Q: 8. What is the derivative of y= Vu in terms of x? dy a) 2/y dulas b) 2vu d) 2/u

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Q: The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 75/(4 + x + y), where…

A: Given that the temperature at a point x, y is Tx, y=754+x2+y2 where T is measured in °C and x, y in…