What is (\partial)/(\partial x)(6xy+5yz+xz-48) ?

The answer to (\partial)/(\partial x)(6xy+5yz+xz-48) is 6y+z

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(\partial)/(\partial x)(6xy+5yz+xz-48)

\frac{\partial}{\partial x} (6 x y + 5 yz + x z - 48)

6 y + z

Solution steps

\frac{\partial}{\partial x} (6 x y + 5 yz + x z - 48)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (5 yz) + \frac{\partial}{\partial x} (x z) - \frac{\partial}{\partial x} (48)

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (5 yz) = 0

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

\frac{\partial}{\partial x} (48) = 0

= 6 y + 0 + z - 0

Simplify

= 6 y + z

16 y^{^{''}} + 152 y^{^{'}} + 361 y = 0, y (0) = 9, y^{^{'}} (0) = 2

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

\int \frac{18}{( x ^{2} - 1 ) ^{2}} d x

y^{^{'}} + 7 x^{- 1} y = x^{2}

10 arcsin (e^{\frac{x}{2}})

What is (\partial)/(\partial x)(6xy+5yz+xz-48) ?
The answer to (\partial)/(\partial x)(6xy+5yz+xz-48) is 6y+z