What is (\partial)/(\partial x)(4xy+yz+5xz-40) ?

The answer to (\partial)/(\partial x)(4xy+yz+5xz-40) is 4y+5z

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(\partial)/(\partial x)(4xy+yz+5xz-40)

\frac{\partial}{\partial x} (4 x y + yz + 5 x z - 40)

4 y + 5 z

Solution steps

\frac{\partial}{\partial x} (4 x y + yz + 5 x z - 40)

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} (5 x z) - \frac{\partial}{\partial x} (40)

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

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

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

\frac{\partial}{\partial x} (40) = 0

= 4 y + 0 + 5 z - 0

Simplify

= 4 y + 5 z

\int - 5 e^{2 x} d x

\int (e^{2 x} - 3)^{2} d x

\int_{- π}^{0} sin^{2} (x) d x

\int \frac{1}{x ^{2} + 4 x + 40} d x

\int \frac{1}{x ^{2} - 9} d x

What is (\partial)/(\partial x)(4xy+yz+5xz-40) ?
The answer to (\partial)/(\partial x)(4xy+yz+5xz-40) is 4y+5z