What is (\partial)/(\partial x)(xyz+9x+8y-4z) ?

The answer to (\partial)/(\partial x)(xyz+9x+8y-4z) is yz+9

(\partial)/(\partial x)(xyz+9x+8y-4z)

\frac{\partial}{\partial x} (x yz + 9 x + 8 y - 4 z)

yz + 9

Solution steps

\frac{\partial}{\partial x} (x yz + 9 x + 8 y - 4 z)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x yz) + \frac{\partial}{\partial x} (9 x) + \frac{\partial}{\partial x} (8 y) - \frac{\partial}{\partial x} (4 z)

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

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

\frac{\partial}{\partial x} (8 y) = 0

\frac{\partial}{\partial x} (4 z) = 0

= yz + 9 + 0 - 0

Simplify

= yz + 9

l a pl a ce t r an s f or m f (t) = 1

in v erse l a pl a ce \frac{s}{( s + 1 ) ^{5}}

\int sin^{3} (3 x) cos^{5} (3 x) d x

\int_{- 2}^{14} \frac{1}{( x + 2 ) ^{\frac{1}{4}}} d x

\int \frac{x ^{3}}{x} d x

What is (\partial)/(\partial x)(xyz+9x+8y-4z) ?
The answer to (\partial)/(\partial x)(xyz+9x+8y-4z) is yz+9