What is (\partial)/(\partial x)(ye^{3x}*3) ?

The answer to (\partial)/(\partial x)(ye^{3x}*3) is 9e^{3x}y

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(\partial)/(\partial x)(ye^{3x}*3)

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

9 e^{3 x} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y \cdot 3 \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

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

Simplify

= 9 e^{3 x} y

y = \frac{7}{x ^{2} + 3}, (2, 1)

x \to 2 lim (x^{3} + 4 x^{2} - 3 x - 6)

\int \frac{1}{t ^{2} 5 - t ^{2}} d t

\int_{1}^{4} \frac{3}{x ^{2}} d x

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

What is (\partial)/(\partial x)(ye^{3x}*3) ?
The answer to (\partial)/(\partial x)(ye^{3x}*3) is 9e^{3x}y