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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Simplify

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

\int z sin (8 z) d z

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

\frac{d}{d x} (arcsin (5 x + 1))

n = 0 \sum \infty \frac{e n}{3 n + 1}

\frac{6}{x}

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