Find the directional derivative of the function at the point P in the direction the unit vector u = cos ôi + sin 0j. Sketch each the graph of the function, t point P, and the unit vector u. 2. f(x, y) = sin(2x + y), P(0, 1), 0 = -. %3D

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Q: 17. f(y) 2 3 your 1³

A: Given, .

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A: Given function is fx =px3 +qx2 +r x The function has an inflection point at (1, 2). The slope of the…

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A: As per the guidelines we can solve 3 problems only.

Q: Find the derivative of the function. y-글xV81- x2 + 81 arcsin(종)|

A: It is given that, y=12x81-x2+81 arcsinx9 We have to find the derivative of the function.

Q: y = CLe? + C2 ze? (3) Differentiate with sespect to 'x' get we dy Again differentiate with sespect…

A: Some results are required to understand the differentiation in the given problem.

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A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

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A: Simply take the derivative of the given equation and simplify.

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A: Please see the below picture for detailed solution.

Q: Find the derivative of the function. y-글|xV81- x2 + 81 arcsin(송)

A: Given,          y=12x81-x2+81arcsinx9

Q: 5. Find y" of 2y – 5x = 3x – 8y

A: 2y-5x=3x-8y

Q: Direction: Find the equation of the tangent line to the function at x=a. 3. y = V5x + 4 at x= 1 4. y…

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Q: 1. Find for the following by implicit differentiation: dy dx 18x9-5 cot y = y² - 18x

A: Given:  1) 18x9-5cot y=y9-18x Implicit differentiation:    Differentiating on both sides…

Q: draw the function and its derivatives. explains why of its derivatives:   y=cosx

A: Given y=cosx