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

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

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

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

9 y^{6} cos (3 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= 9 y^{6} cos (3 x)

13 sin (x)

f (x) = \frac{1}{x + 4}

x \to 0 lim (\frac{3}{x})

\frac{\partial}{\partial x} (\frac{61}{7 + x ^{2} + y ^{2}})

x \to 3 lim (\frac{x ^{2} + 1}{x - 3})

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