What is (\partial)/(\partial x)(x^4ey^z) ?

The answer to (\partial)/(\partial x)(x^4ey^z) is 4ex^3y^z

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(\partial)/(\partial x)(x^4ey^z)

\frac{\partial}{\partial x} (x^{4} e y^{z})

4 e x^{3} y^{z}

Solution steps

\frac{\partial}{\partial x} (x^{4} e y^{z})

Treat

y, z

as constants

Take the constant out:

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

= e y^{z} \frac{\partial}{\partial x} (x^{4})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= e y^{z} \cdot 4 x^{4 - 1}

Simplify

= 4 e x^{3} y^{z}

\frac{d}{d x} (\frac{( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 )})

\frac{d}{d x} (1.8 x + 2.5)

\int \frac{5 x + 1}{( 2 x + 1 ) ( x - 1 )} d x

\int \frac{x ^{3}}{( x ^{2} + 1 ) ^{3}} d x

\int \frac{1}{1 - z ^{2}} d z

What is (\partial)/(\partial x)(x^4ey^z) ?
The answer to (\partial)/(\partial x)(x^4ey^z) is 4ex^3y^z