What is (\partial)/(\partial x)(x^2y^2(2z+1)^2) ?

The answer to (\partial)/(\partial x)(x^2y^2(2z+1)^2) is 2xy^2(2z+1)^2

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(\partial)/(\partial x)(x^2y^2(2z+1)^2)

\frac{\partial}{\partial x} (x^{2} y^{2} (2 z + 1)^{2})

2 x y^{2} (2 z + 1)^{2}

Solution steps

\frac{\partial}{\partial x} (x^{2} y^{2} (2 z + 1)^{2})

Treat

y, z

as constants

Take the constant out:

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

= y^{2} (2 z + 1)^{2} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

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

= y^{2} (2 z + 1)^{2} \cdot 2 x^{2 - 1}

Simplify

= 2 x y^{2} (2 z + 1)^{2}

\int \frac{x ^{2}}{a ^{2} + b ^{2}} d x

\int \frac{x ^{2} - x}{x ^{3} - 6 x ^{2} + 11 x - 6} d x

\int_{0}^{5} \frac{4 t}{( t - 6 ) ^{2}} d t

\int \frac{( 4 u ^{2} - 8 )}{2 u ^{2} + 1} d u

\frac{d}{d x} (\frac{x ^{2}}{4 - x ^{2}})

What is (\partial)/(\partial x)(x^2y^2(2z+1)^2) ?
The answer to (\partial)/(\partial x)(x^2y^2(2z+1)^2) is 2xy^2(2z+1)^2