Resolved: "Find the indicate d partial derivative.f(x,y)=ysin−1(xy);fy(1,12)" - Plainmath

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2022-08-18

Find the indicate d partial derivative.

f (x, y) = y \sin^{- 1} (x y); f_{y} (1, \frac{1}{2})

Answer & Explanation

Helena Ward

Beginner2022-08-19Added 11 answers

f (x, y) = y \sin^{- 1} x y

Differentiate with respect to y, treat x like a constants

f_{y} (x, y) = \sin^{- 1} x y + y \cdot \frac{1}{\sqrt{1 - x^{2} y^{2}}} \cdot x

f_{y} (x, y) = \sin^{- 1} x y + \frac{x y}{\sqrt{1 - x^{2} y^{2}}}

Therefore

f_{y} (1, \frac{1}{2}) = \sin^{- 1} \frac{1}{2} + \frac{\frac{1}{2}}{\sqrt{1 - \frac{1}{4}}}

f_{y} (1, \frac{1}{2}) = \frac{π}{6} + \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}

f_{y} (1, \frac{1}{2}) = \frac{π}{6} + \frac{1}{\sqrt{3}}

Result:

f_{y} (1, \frac{1}{2}) = \frac{π}{6} + \frac{1}{\sqrt{3}}

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