What is (\partial)/(\partial x)((y)(y^5-3xy)) ?

The answer to (\partial)/(\partial x)((y)(y^5-3xy)) is -3y^2

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(\partial)/(\partial x)((y)(y^5-3xy))

\frac{\partial}{\partial x} ((y) (y^{5} - 3 x y))

- 3 y^{2}

Solution steps

\frac{\partial}{\partial x} ((y) (y^{5} - 3 x y))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (y^{5} - 3 x y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= y (\frac{\partial}{\partial x} (y^{5}) - \frac{\partial}{\partial x} (3 x y))

\frac{\partial}{\partial x} (y^{5}) = 0

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

= y (0 - 3 y)

Simplify

y (0 - 3 y) : - 3 y^{2}

= - 3 y^{2}

\frac{5 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

(u + v) d u

15 (\frac{2}{5} - 3 x)

15 (\frac{2}{5} - 3 v)

(x - a + x - a)^{2}

What is (\partial)/(\partial x)((y)(y^5-3xy)) ?
The answer to (\partial)/(\partial x)((y)(y^5-3xy)) is -3y^2