What is the derivative of (8x^{1/2}) ?

The derivative of (8x^{1/2}) is (2/x)^{1/2}

What is the first derivative of (8x^{1/2}) ?

The first derivative of (8x^{1/2}) is (2/x)^{1/2}

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\frac{d}{d x} ((8 x)^{\frac{1}{2}})

(\frac{2}{x})^{\frac{1}{2}}

Solution steps

\frac{d}{d x} ((8 x)^{\frac{1}{2}})

Simplify

(8 x)^{\frac{1}{2}} : 8^{\frac{1}{2}} x^{\frac{1}{2}}

= \frac{d}{d x} (8^{\frac{1}{2}} x^{\frac{1}{2}})

Take the constant out:

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

= 8^{\frac{1}{2}} \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 8^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

8^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : (\frac{2}{x})^{\frac{1}{2}}

= (\frac{2}{x})^{\frac{1}{2}}

\frac{\partial}{\partial x} (3 \cdot (y + 1) \cdot (x - 3)^{3})

\int (x^{2} - 4)^{3} x d x

n = 1 \sum \infty \frac{- 4 ^{n}}{4 ^{n}}

\int_{0}^{\infty} e^{- 0.8 x} d x

y^{^{''}} + 8 y^{^{'}} + 32 y = 32, y (0) = 2, y^{^{'}} (0) = - 20

What is the derivative of (8x^{1/2}) ?
The derivative of (8x^{1/2}) is (2/x)^{1/2}
What is the first derivative of (8x^{1/2}) ?
The first derivative of (8x^{1/2}) is (2/x)^{1/2}