What is (\partial)/(\partial x)(8ye^{5x}) ?

The answer to (\partial)/(\partial x)(8ye^{5x}) is 40e^{5x}y

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(\partial)/(\partial x)(8ye^{5x})

\frac{\partial}{\partial x} (8 y e^{5 x})

40 e^{5 x} y

Solution steps

\frac{\partial}{\partial x} (8 y e^{5 x})

Treat

y

as a constant

Take the constant out:

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

= 8 y \frac{\partial}{\partial x} (e^{5 x})

Apply the chain rule:

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

= e^{5 x} \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= 8 y e^{5 x} \cdot 5

Simplify

= 40 e^{5 x} y

\int \frac{5 ^{- x}}{ln ( 5 )} d x

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

arcsin (sin (5 x))

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

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

What is (\partial)/(\partial x)(8ye^{5x}) ?
The answer to (\partial)/(\partial x)(8ye^{5x}) is 40e^{5x}y