What is (\partial)/(\partial x)(5x^2-3xy+xyz) ?

The answer to (\partial)/(\partial x)(5x^2-3xy+xyz) is 10x-3y+yz

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(\partial)/(\partial x)(5x^2-3xy+xyz)

\frac{\partial}{\partial x} (5 x^{2} - 3 x y + x yz)

10 x - 3 y + yz

Solution steps

\frac{\partial}{\partial x} (5 x^{2} - 3 x y + x yz)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{2}) - \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (x yz)

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

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

= 10 x - 3 y + yz

- 2 t^{3}

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

x \to 0 lim (x^{2} sin (x))

\int - 5 sin (5 t) d t

y^{3}

What is (\partial)/(\partial x)(5x^2-3xy+xyz) ?
The answer to (\partial)/(\partial x)(5x^2-3xy+xyz) is 10x-3y+yz