Determine the directional derivative of the function f(x, y) = (5x³ 7y±+15xy)/T in the direction given by the curve r(t) = (3n cos(2t), 5 sin(2t)) at the point given by t=a.

Q: Find the directional derivative of the function f (x, y) = ln (x + 2y) at the point P(1/4, 1/8) in…

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Q: Find the equation of the tangent line to sin (x – 2y) = 2xy – 1 2лу — (1.:) at the point ( 1,

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Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

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Q: Consider the curve given by the equation eªy + x² cos y cos y = 3x - y +2. 0). Find y/(0) (i.e. the…

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Q: 2. Answer the following derivative related questions. dy. (1) Let y = x' + 4x³ + 2x² + 16, find ; dx…

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Q: Use implicit differentiation to find dz/dx and dz/dy. X - z = arctan(yz) 218 дх 3: ду = = 1 22 yz +1…

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Q: Determine the second derivative of the parametrically defined curve represented by the equations…

A: dsintdt=costdcostdt=-sintdydx=dydtdxdt

Q: Find the derivative dydx of the parametrically defined function x=t+2sinπt, y=3t−cosπt at t=12

A: Given X=t+ 2 sinπt        and   y = 3t- cosπt We have to find dy/dx at t=12 Method used  Chain…

Q: nd the points at which f(x) = cos² x has a horizontal tangent line. %3D

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Q: f2(x) = (4x + 5)°, fa(x)= (2x² +x)VI, fa(x) cos(3r) – 2 sin? x, COS

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Q: Find the second derivative of y, where y = t² sint.

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Q: Find the derivative (dy/dx) of the following functions: a) xy = cotxy %3D

A: Since you have asked different multiple question, we will solve the first question for you. . If you…

Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: The slope of the tangent line to the curve parametrized by the equations x (t) = -2(cos(t) + t…

A: Slope of tangent is equal to dy/dx.

Q: Hew-2 Find the directionat derivative of the funCtion X+XCos7-y Sinz +yat the faint Pe (2,=ly0…

A: Answer is following-