What is implicit (dy)/(dx),15x=15y+5y^3+3y^5 ?

The answer to implicit (dy)/(dx),15x=15y+5y^3+3y^5 is (dy)/(dx)= 1/(1+y^2+y^4)

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implicit (dy)/(dx),15x=15y+5y^3+3y^5

implicit derivative

\frac{d y}{d x}, 15 x = 15 y + 5 y^{3} + 3 y^{5}

\frac{d y}{d x} = \frac{1}{1 + y ^{2} + y ^{4}}

Solution steps

15 x = 15 y + 5 y^{3} + 3 y^{5}

Treat

y

y (x)

Differentiate both sides:

15 = 15 \frac{d y}{d x} + 15 y^{2} \frac{d y}{d x} + 15 y^{4} \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{1 + y ^{2} + y ^{4}}

\frac{d y}{d x} = \frac{1}{1 + y ^{2} + y ^{4}}

y^{^{'}} + \frac{y}{x} = 5 \cdot x^{3}

\frac{d}{d x} (e^{- 2 x} \cdot sin (x))

\int 1 + e^{2 x} d x

\frac{d}{d x} (ln ((x^{2} + 4 x + 5)^{3}))

\int e - e^{x} d x

What is implicit (dy)/(dx),15x=15y+5y^3+3y^5 ?
The answer to implicit (dy)/(dx),15x=15y+5y^3+3y^5 is (dy)/(dx)= 1/(1+y^2+y^4)