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

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

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

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

y e^{3 x} \cdot 3

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 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

= y e^{3 x} \cdot 3

\frac{d}{d x} (- 2 (2 x^{2} - 4 x - 1)^{2})

\frac{\partial}{\partial x} (2)

t \cdot y^{^{'}} + 4 y = 8 t

y^{^{''}} + 3 y^{^{'}} - 4 y = e^{- 4 x} + x e^{- x}

\frac{\partial}{\partial x} (z^{x y^{2}})

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