What is (\partial)/(\partial x)(4ysqrt(x)) ?

The answer to (\partial)/(\partial x)(4ysqrt(x)) is (2y)/(sqrt(x))

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(\partial)/(\partial x)(4ysqrt(x))

\frac{\partial}{\partial x} (4 y x)

\frac{2 y}{x}

Solution steps

\frac{\partial}{\partial x} (4 y x)

Treat

y

as a constant

Take the constant out:

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

= 4 y \frac{\partial}{\partial x} (x)

Apply radical rule:

a = a^{\frac{1}{2}}

= 4 y \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 4 y \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

4 y \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{2 y}{x}

= \frac{2 y}{x}

y^{^{'}} = 5 x e^{y}, y (0) = 0

\int_{0}^{\infty} x e^{- 4 x} d x

\int \frac{1}{x ^{2} - 256} d x

x \to - 7 lim (∣ x + 7 ∣)

\frac{d}{d x} (20)

What is (\partial)/(\partial x)(4ysqrt(x)) ?
The answer to (\partial)/(\partial x)(4ysqrt(x)) is (2y)/(sqrt(x))