What is (\partial)/(\partial x)(2xy+yz+5xz-32) ?

The answer to (\partial)/(\partial x)(2xy+yz+5xz-32) is 2y+5z

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(\partial)/(\partial x)(2xy+yz+5xz-32)

\frac{\partial}{\partial x} (2 x y + yz + 5 x z - 32)

2 y + 5 z

Solution steps

\frac{\partial}{\partial x} (2 x y + yz + 5 x z - 32)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (yz) + \frac{\partial}{\partial x} (5 x z) - \frac{\partial}{\partial x} (32)

\frac{\partial}{\partial x} (2 x y) = 2 y

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

\frac{\partial}{\partial x} (5 x z) = 5 z

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

= 2 y + 0 + 5 z - 0

Simplify

= 2 y + 5 z

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

\frac{d}{d x} (- \frac{6 x}{( x ^{2} - 4 ) ^{2}})

\int sin (2 x) cos (3 x) d x

x^{3} - 7 x^{2}

y = \frac{5}{π} + \frac{4}{x ^{2} + 9}

What is (\partial)/(\partial x)(2xy+yz+5xz-32) ?
The answer to (\partial)/(\partial x)(2xy+yz+5xz-32) is 2y+5z