What is the derivative of xe^{3y} ?

The derivative of xe^{3y} is e^{3y}+3e^{3y}x(dy)/(dx)

What is the first derivative of xe^{3y} ?

The first derivative of xe^{3y} is e^{3y}+3e^{3y}x(dy)/(dx)

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

e^{3 y} + 3 e^{3 y} x \frac{d y}{d x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{3 y}

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{3 y} + e^{3 y} \cdot 3 \frac{d y}{d x} x

Simplify

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

\frac{1}{t} y^{^{'}} = \frac{y}{t ^{2}} - \frac{1}{y}

\frac{\partial}{\partial y} (5 y - 2 x)

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 100 cos (8 t)

(2 x - 1) d x + (7 y + 5) d y = 0

\frac{d}{d x} (2 e^{x - 1})

What is the derivative of xe^{3y} ?
The derivative of xe^{3y} is e^{3y}+3e^{3y}x(dy)/(dx)
What is the first derivative of xe^{3y} ?
The first derivative of xe^{3y} is e^{3y}+3e^{3y}x(dy)/(dx)