What is (\partial)/(\partial x)(5ye^{4x}) ?

The answer to (\partial)/(\partial x)(5ye^{4x}) is 20e^{4x}y

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(\partial)/(\partial x)(5ye^{4x})

\frac{\partial}{\partial x} (5 y e^{4 x})

20 e^{4 x} y

Solution steps

\frac{\partial}{\partial x} (5 y e^{4 x})

Treat

y

as a constant

Take the constant out:

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

= 5 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

= 5 y e^{4 x} \cdot 4

Simplify

= 20 e^{4 x} y

(- 2, 3), (2, - 2)

\frac{d v}{d t} = v^{2} + 5 v + 2

\frac{d}{d x} (\frac{4}{3} x^{3} + \frac{1}{2} x - 4)

\int \frac{6 e ^{6 t}}{9 + e ^{6 t}} d t

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

What is (\partial)/(\partial x)(5ye^{4x}) ?
The answer to (\partial)/(\partial x)(5ye^{4x}) is 20e^{4x}y