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

The answer to (\partial)/(\partial x)((z)(x^2e^y+10y)) is 2e^yzx

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

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

2 e^{y} z x

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (10 y) = 0

= z (2 e^{y} x + 0)

Simplify

= 2 e^{y} z x

(2 + 4 i)^{3}

\frac{4 ( 6 + 3 )}{33}

- 2 (2 + 34)

\frac{( - n ^{2} - 3 n )}{2 ( 1 - 2 n )}

\frac{( 2 x ^{3} - 4 x ^{2} - 15 x + 4 )}{( x - 1 ) ^{2}}

What is (\partial)/(\partial x)((z)(x^2e^y+10y)) ?
The answer to (\partial)/(\partial x)((z)(x^2e^y+10y)) is 2e^yzx