What is (\partial)/(\partial x)(y^6cos(6x)*6) ?

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

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(\partial)/(\partial x)(y^6cos(6x)*6)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y^{6} \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

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

Simplify

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

y = \frac{1}{( 7 x + 16 ) ^{4}}

7 sec (x)

\frac{\partial}{\partial x} (\frac{y}{y - 4 x})

\frac{( e ^{x} )}{1 + x}

x \to \infty lim (\frac{x ^{4}}{e ^{- 6 x}})

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