What is implicit (dy)/(dx),5+4x=sin(xy^3) ?

The answer to implicit (dy)/(dx),5+4x=sin(xy^3) is (dy)/(dx)=(4-y^3cos(xy^3))/(3xy^2cos(xy^3))

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implicit (dy)/(dx),5+4x=sin(xy^3)

implicit derivative

\frac{d y}{d x}, 5 + 4 x = sin (x y^{3})

\frac{d y}{d x} = \frac{4 - y ^{3} cos ( x y ^{3} )}{3 x y ^{2} cos ( x y ^{3} )}

Solution steps

5 + 4 x = sin (x y^{3})

Treat

y

y (x)

Differentiate both sides:

4 = cos (x y^{3}) (y^{3} + 3 x y^{2} \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4 - y ^{3} cos ( x y ^{3} )}{3 x y ^{2} cos ( x y ^{3} )}

\frac{d y}{d x} = \frac{4 - y ^{3} cos ( x y ^{3} )}{3 x y ^{2} cos ( x y ^{3} )}

What is implicit (dy)/(dx),5+4x=sin(xy^3) ?
The answer to implicit (dy)/(dx),5+4x=sin(xy^3) is (dy)/(dx)=(4-y^3cos(xy^3))/(3xy^2cos(xy^3))