What is (\partial)/(\partial x)(z^4x^{0.5}) ?

The answer to (\partial)/(\partial x)(z^4x^{0.5}) is (0.5z^4)/(x^{0.5)}

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(\partial)/(\partial x)(z^4x^{0.5})

\frac{\partial}{\partial x} (z^{4} x^{0.5})

\frac{0.5 z ^{4}}{x ^{0.5}}

Solution steps

\frac{\partial}{\partial x} (z^{4} x^{0.5})

Treat

z

as a constant

Take the constant out:

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

= z^{4} \frac{\partial}{\partial x} (x^{0.5})

Apply the Power Rule:

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

= z^{4} \cdot 0.5 x^{0.5 - 1}

Simplify

z^{4} \cdot 0.5 x^{0.5 - 1} : \frac{0.5 z ^{4}}{x ^{0.5}}

= \frac{0.5 z ^{4}}{x ^{0.5}}

\frac{d y}{d x} = (2 x + 1) (y + 1), y (- 1) = 1

\frac{d y}{d x} = y (5 x^{2} + 3)

\int_{1}^{4} \frac{4}{x ^{2}} d x

x \to 0 + lim (x^{\frac{2}{x}})

h \to 1 lim (4 h^{2})

What is (\partial)/(\partial x)(z^4x^{0.5}) ?
The answer to (\partial)/(\partial x)(z^4x^{0.5}) is (0.5z^4)/(x^{0.5)}