What is (\partial)/(\partial x)(e^{3x}dy) ?

The answer to (\partial)/(\partial x)(e^{3x}dy) is dye^{3x}*3

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(\partial)/(\partial x)(e^{3x}dy)

\frac{\partial}{\partial x} (e^{3 x} d y)

d y e^{3 x} \cdot 3

Solution steps

\frac{\partial}{\partial x} (e^{3 x} d y)

Treat

d, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= d y \frac{\partial}{\partial x} (e^{3 x})

Apply the chain rule:

e^{3 x} \frac{\partial}{\partial x} (3 x)

= e^{3 x} \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= d y e^{3 x} \cdot 3

\frac{\partial}{\partial x} (x^{2} + 6 x y + y^{2})

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0, y (0) = 9

\frac{\partial}{\partial y} (2 x^{2} + 4 y^{2} + \frac{1}{2})

y^{^{'}} = 1 + y

\int_{0}^{1} \frac{1}{x - 1} d x

What is (\partial)/(\partial x)(e^{3x}dy) ?
The answer to (\partial)/(\partial x)(e^{3x}dy) is dye^{3x}*3