What is (\partial)/(\partial x)(5xy(15-x-y)) ?

The answer to (\partial)/(\partial x)(5xy(15-x-y)) is 5y(-2x-y+15)

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(\partial)/(\partial x)(5xy(15-x-y))

\frac{\partial}{\partial x} (5 x y (15 - x - y))

5 y (- 2 x - y + 15)

Solution steps

\frac{\partial}{\partial x} (5 x y (15 - x - y))

Treat

y

as a constant

Take the constant out:

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

= 5 y \frac{\partial}{\partial x} (x (15 - x - y))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 15 - x - y

= 5 y (\frac{\partial}{\partial x} (x) (15 - x - y) + \frac{\partial}{\partial x} (15 - x - y) x)

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

\frac{\partial}{\partial x} (15 - x - y) = - 1

= 5 y (1 \cdot (15 - x - y) + (- 1) x)

Simplify

5 y (1 \cdot (15 - x - y) + (- 1) x) : 5 y (- 2 x - y + 15)

= 5 y (- 2 x - y + 15)

15 e^{x^{2}}

y^{^{'}} + 2 y = 4 sin (e^{2 x})

y^{^{'}} = \frac{( e ^{- x} - e ^{x} )}{( 3 + 4 y )}, y (0) = 1

(0, - 9), (- 1, - 4)

\frac{d y}{d x} = cos^{2} (x)

What is (\partial)/(\partial x)(5xy(15-x-y)) ?
The answer to (\partial)/(\partial x)(5xy(15-x-y)) is 5y(-2x-y+15)