What is implicit sin(y)=5x^3-5 ?

The answer to implicit sin(y)=5x^3-5 is (dy)/(dx)=(15x^2)/(cos(y))

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implicit sin(y)=5x^3-5

implicit derivative

sin (y) = 5 x^{3} - 5

\frac{d y}{d x} = \frac{15 x ^{2}}{cos ( y )}

Solution steps

sin (y) = 5 x^{3} - 5

Treat

y

y (x)

Differentiate both sides:

cos (y) \frac{d y}{d x} = 15 x^{2}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{15 x ^{2}}{cos ( y )}

\frac{d y}{d x} = \frac{15 x ^{2}}{cos ( y )}

f (x) = x^{2} - x + 1, at x = - 1

h \to 0 lim (6 x + 3 h)

\frac{d}{d x} (1 + 2 x)

\frac{\partial}{\partial x} (x y^{2} + x)

\frac{d y}{d x} - y x - y^{2} = 0

What is implicit sin(y)=5x^3-5 ?
The answer to implicit sin(y)=5x^3-5 is (dy)/(dx)=(15x^2)/(cos(y))