What is (\partial)/(\partial x)(x^2+10xyz+y^2+8z^2) ?

The answer to (\partial)/(\partial x)(x^2+10xyz+y^2+8z^2) is 2x+10yz

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(\partial)/(\partial x)(x^2+10xyz+y^2+8z^2)

\frac{\partial}{\partial x} (x^{2} + 10 x yz + y^{2} + 8 z^{2})

2 x + 10 yz

Solution steps

\frac{\partial}{\partial x} (x^{2} + 10 x yz + y^{2} + 8 z^{2})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (10 x yz) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (8 z^{2})

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

\frac{\partial}{\partial x} (10 x yz) = 10 yz

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (8 z^{2}) = 0

= 2 x + 10 yz + 0 + 0

Simplify

= 2 x + 10 yz

\frac{d}{d x} (arctanh (cos (x)))

\frac{d}{d x} (x - 3 y)

e^{- 2 x^{2}}

x = - y^{2} + 2, x = y^{2} - 4

\int_{- 2}^{3} \frac{42}{x ^{4}} d x

What is (\partial)/(\partial x)(x^2+10xyz+y^2+8z^2) ?
The answer to (\partial)/(\partial x)(x^2+10xyz+y^2+8z^2) is 2x+10yz