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Juli2301 [7.4K]
3 years ago
10

If sin(xy)=x, then find dy/dx

Mathematics
2 answers:
emmainna [20.7K]3 years ago
5 0
We are given the expression sin (xy) = x and is asked for the dy/dx. we can use implicit differentiation to differentiate the function. sin (xy) = xcos (xy) *(x dy + y dx) = dxdx (cos (xy) * y - 1 ) = -x* cos (xy) dydy/dx = -(cos (xy) * y - 1 )/x* cos (xy)dy/dx = -1/x + 1/x cos (xy) 
Andrews [41]3 years ago
3 0
Let u = xy
now dy/dx(sin(u))
= cos(u)
=cos(dy/dx(xy))
= cos(xy)y
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Option C

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