What is (\partial)/(\partial x)(3y^6cos(3x)) ?

The answer to (\partial)/(\partial x)(3y^6cos(3x)) is -9y^6sin(3x)

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(\partial)/(\partial x)(3y^6cos(3x))

\frac{\partial}{\partial x} (3 y^{6} cos (3 x))

- 9 y^{6} sin (3 x)

Solution steps

\frac{\partial}{\partial x} (3 y^{6} cos (3 x))

Treat

y

as a constant

Take the constant out:

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

= 3 y^{6} \frac{\partial}{\partial x} (cos (3 x))

Apply the chain rule:

- sin (3 x) \frac{\partial}{\partial x} (3 x)

= - sin (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= 3 y^{6} (- sin (3 x) \cdot 3)

Simplify

= - 9 y^{6} sin (3 x)

\frac{\partial}{\partial x} (2 e^{x y^{2}})

\int \frac{( 3 x - 1 )}{x x ^{2} - 4} d x

x \to 1 lim (7^{x^{4} - x^{2}})

\int_{0}^{1} ln (x + 1) d x

\frac{d}{d x} ((3 + 4 x - x^{2})^{\frac{1}{2}})

What is (\partial)/(\partial x)(3y^6cos(3x)) ?
The answer to (\partial)/(\partial x)(3y^6cos(3x)) is -9y^6sin(3x)