What is implicit (dy)/(dx),e^{5y^2}=x^3+3 ?

The answer to implicit (dy)/(dx),e^{5y^2}=x^3+3 is (dy)/(dx)=(3x^2)/(e^{5y^2)*10y}

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implicit (dy)/(dx),e^{5y^2}=x^3+3

implicit derivative

\frac{d y}{d x}, e^{5 y^{2}} = x^{3} + 3

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{5 y^{2}} \cdot 10 y}

Solution steps

e^{5 y^{2}} = x^{3} + 3

Treat

y

y (x)

Differentiate both sides:

e^{5 y^{2}} \cdot 10 y \frac{d y}{d x} = 3 x^{2}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{3 x ^{2}}{e ^{5 y^{2}} \cdot 10 y}

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{5 y^{2}} \cdot 10 y}

y^{^{'}} = (x - 2) e^{- 2 y}, y (2) = ln (2)

\frac{\partial}{\partial y} (x e^{\frac{x}{y}})

\int_{25}^{50} 20 d x

f (x) = \frac{x ^{2} + 1}{x + 4}

f (x) = x^{\frac{5}{2}} (2 - 5 x^{3})

What is implicit (dy)/(dx),e^{5y^2}=x^3+3 ?
The answer to implicit (dy)/(dx),e^{5y^2}=x^3+3 is (dy)/(dx)=(3x^2)/(e^{5y^2)*10y}