What is (\partial)/(\partial y)(15-5(y+3)^2) ?

The answer to (\partial)/(\partial y)(15-5(y+3)^2) is -10y-30

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(\partial)/(\partial y)(15-5(y+3)^2)

\frac{\partial}{\partial y} (15 - 5 (y + 3)^{2})

- 10 y - 30

Solution steps

\frac{\partial}{\partial y} (15 - 5 (y + 3)^{2})

Simplify

15 - 5 (y + 3)^{2} : - 5 y^{2} - 30 y - 30

= \frac{\partial}{\partial y} (- 5 y^{2} - 30 y - 30)

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial y} (5 y^{2}) - \frac{\partial}{\partial y} (30 y) - \frac{\partial}{\partial y} (30)

\frac{\partial}{\partial y} (5 y^{2}) = 10 y

\frac{\partial}{\partial y} (30 y) = 30

\frac{\partial}{\partial y} (30) = 0

= - 10 y - 30 - 0

Simplify

= - 10 y - 30

\frac{\partial}{\partial x} (7 x^{3} cos (7 x^{2} y))

\frac{\partial}{\partial y} (3 x^{4} y^{2} + 1)

\int_{- 2}^{3} \frac{22}{x ^{4}} d x

\frac{1}{3}

\int 343 x^{2} cos (7 x) d x

What is (\partial)/(\partial y)(15-5(y+3)^2) ?
The answer to (\partial)/(\partial y)(15-5(y+3)^2) is -10y-30