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

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

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(\partial)/(\partial y)((y-5)(x+5)^2)

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

(x + 5)^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (y) = 1

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

= (x + 5)^{2} (1 - 0)

Simplify

= (x + 5)^{2}

\frac{d}{d x} (x^{4} - 20 x^{2} + 64)

\int 8 cos^{3} (2 θ) sin (2 θ) d θ

x \to 0 lim (\frac{tan ( a x )}{x})

\frac{d}{d x} (\frac{1}{2} sin (x) cos (x))

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 5 y^{3})

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