What is (\partial)/(\partial x)(z^2x^3) ?

The answer to (\partial)/(\partial x)(z^2x^3) is 3z^2x^2

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(\partial)/(\partial x)(z^2x^3)

\frac{\partial}{\partial x} (z^{2} x^{3})

3 z^{2} x^{2}

Solution steps

\frac{\partial}{\partial x} (z^{2} x^{3})

Treat

z

as a constant

Take the constant out:

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

= z^{2} \frac{\partial}{\partial x} (x^{3})

Apply the Power Rule:

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

= z^{2} \cdot 3 x^{3 - 1}

Simplify

= 3 z^{2} x^{2}

f (x) = x^{2} + 3

\int 2 arctan (x) d x

f (x) = x^{5} + 4, g (x) = x + 4

f (x) = - \frac{1}{2 1 - x}, at x = - 8

\int \frac{1}{u 7 - u ^{2}} d u

What is (\partial)/(\partial x)(z^2x^3) ?
The answer to (\partial)/(\partial x)(z^2x^3) is 3z^2x^2