What is (\partial)/(\partial x)(e^{-6y}cos(6x)*6) ?

The answer to (\partial)/(\partial x)(e^{-6y}cos(6x)*6) is -36e^{-6y}sin(6x)

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(\partial)/(\partial x)(e^{-6y}cos(6x)*6)

\frac{\partial}{\partial x} (e^{- 6 y} cos (6 x) \cdot 6)

- 36 e^{- 6 y} sin (6 x)

Solution steps

\frac{\partial}{\partial x} (e^{- 6 y} cos (6 x) \cdot 6)

Treat

y

as a constant

Take the constant out:

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

= e^{- 6 y} \cdot 6 \frac{\partial}{\partial x} (cos (6 x))

Apply the chain rule:

- sin (6 x) \frac{\partial}{\partial x} (6 x)

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

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

= e^{- 6 y} \cdot 6 (- sin (6 x) \cdot 6)

Simplify

= - 36 e^{- 6 y} sin (6 x)

\int \frac{3 x}{2 x - 1} d x

2^{2 x}

\int x 4 x^{2} + 1 d x

\frac{d}{d x} (e^{5 x - 4 x^{2}})

\frac{d}{d x} (\frac{x}{7 x + 1})

What is (\partial)/(\partial x)(e^{-6y}cos(6x)*6) ?
The answer to (\partial)/(\partial x)(e^{-6y}cos(6x)*6) is -36e^{-6y}sin(6x)