What is (\partial)/(\partial x)(5ye^{6x}) ?

The answer to (\partial)/(\partial x)(5ye^{6x}) is 30e^{6x}y

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(\partial)/(\partial x)(5ye^{6x})

\frac{\partial}{\partial x} (5 y e^{6 x})

30 e^{6 x} y

Solution steps

\frac{\partial}{\partial x} (5 y e^{6 x})

Treat

y

as a constant

Take the constant out:

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

= 5 y \frac{\partial}{\partial x} (e^{6 x})

Apply the chain rule:

e^{6 x} \frac{\partial}{\partial x} (6 x)

= e^{6 x} \frac{\partial}{\partial x} (6 x)

\frac{\partial}{\partial x} (6 x) = 6

= 5 y e^{6 x} \cdot 6

Simplify

= 30 e^{6 x} y

\frac{d}{d x} (csc (10 x))

y = x^{3} + 3 x^{2}

\frac{\partial}{\partial x} ((x^{5} + x - y)^{6})

y = 9 e^{- x} + e^{2 x}

\int 8 x^{3} - cos (4 x) d x

What is (\partial)/(\partial x)(5ye^{6x}) ?
The answer to (\partial)/(\partial x)(5ye^{6x}) is 30e^{6x}y