What is (\partial)/(\partial x)(4xy+3yz+5xy-48) ?

The answer to (\partial)/(\partial x)(4xy+3yz+5xy-48) is 9y

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(\partial)/(\partial x)(4xy+3yz+5xy-48)

\frac{\partial}{\partial x} (4 x y + 3 yz + 5 x y - 48)

9 y

Solution steps

\frac{\partial}{\partial x} (4 x y + 3 yz + 5 x y - 48)

Simplify

4 x y + 3 yz + 5 x y - 48 : 9 x y + 3 yz - 48

= \frac{\partial}{\partial x} (9 x y + 3 yz - 48)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (9 x y) + \frac{\partial}{\partial x} (3 yz) - \frac{\partial}{\partial x} (48)

\frac{\partial}{\partial x} (9 x y) = 9 y

\frac{\partial}{\partial x} (3 yz) = 0

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

= 9 y + 0 - 0

Simplify

= 9 y

\frac{d}{d x} (x^{n} ln (\frac{1}{x}))

\frac{- 3}{( s - 2 ) ^{2}}

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

\int tan (5 x) d x

\frac{d}{d x} (\frac{x ^{2} - 2 x + 5}{x ^{2} + 9})

What is (\partial)/(\partial x)(4xy+3yz+5xy-48) ?
The answer to (\partial)/(\partial x)(4xy+3yz+5xy-48) is 9y