What is (\partial)/(\partial x)(4xy+yz+3xz-32) ?

The answer to (\partial)/(\partial x)(4xy+yz+3xz-32) is 4y+3z

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(\partial)/(\partial x)(4xy+yz+3xz-32)

\frac{\partial}{\partial x} (4 x y + yz + 3 x z - 32)

4 y + 3 z

Solution steps

\frac{\partial}{\partial x} (4 x y + yz + 3 x z - 32)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (yz) + \frac{\partial}{\partial x} (3 x z) - \frac{\partial}{\partial x} (32)

\frac{\partial}{\partial x} (4 x y) = 4 y

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

\frac{\partial}{\partial x} (3 x z) = 3 z

\frac{\partial}{\partial x} (32) = 0

= 4 y + 0 + 3 z - 0

Simplify

= 4 y + 3 z

\frac{d}{d x} (x^{6} e^{2 x^{3}})

(1 + x^{2})^{\frac{- 3}{2}}

y^{^{'}} = \frac{( 3 y ^{2} + 9 )}{2 x y}

n = 1 \sum \infty \frac{1}{2 + n}

x \to 0 lim (\frac{1 - e ^{2 x}}{x})

What is (\partial)/(\partial x)(4xy+yz+3xz-32) ?
The answer to (\partial)/(\partial x)(4xy+yz+3xz-32) is 4y+3z