What is (\partial)/(\partial x)(ye^{4x}) ?

The answer to (\partial)/(\partial x)(ye^{4x}) is ye^{4x}*4

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(\partial)/(\partial x)(ye^{4x})

\frac{\partial}{\partial x} (y e^{4 x})

y e^{4 x} \cdot 4

Solution steps

\frac{\partial}{\partial x} (y e^{4 x})

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (e^{4 x})

Apply the chain rule:

e^{4 x} \frac{\partial}{\partial x} (4 x)

= e^{4 x} \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= y e^{4 x} \cdot 4

\int_{1}^{5} \frac{ln ( x )}{x ^{7}} d x

\frac{d}{d x} (\frac{3}{2} x^{\frac{5}{3}} - \frac{5 x}{4} + 7 x^{2} - \frac{6}{x ^{5}} + 6)

y = (3 x - 2 x^{2})^{3} \frac{d y}{d x}

\frac{d y}{d x} = x^{7} e^{x^{8}}

x \to 0 lim (x e^{\frac{1}{x}})

What is (\partial)/(\partial x)(ye^{4x}) ?
The answer to (\partial)/(\partial x)(ye^{4x}) is ye^{4x}*4