What is (\partial)/(\partial x)(16sqrt(3x)) ?

The answer to (\partial)/(\partial x)(16sqrt(3x)) is (8sqrt(3))/(sqrt(x))

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(\partial)/(\partial x)(16sqrt(3x))

\frac{\partial}{\partial x} (16 3 x)

\frac{8 3}{x}

Solution steps

\frac{\partial}{\partial x} (16 3 x)

Simplify

16 3 x : 163 x

= \frac{\partial}{\partial x} (163 x)

Take the constant out:

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

= 163 \frac{\partial}{\partial x} (x)

Apply radical rule:

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

= 163 \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 163 \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

163 \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{8 3}{x}

= \frac{8 3}{x}

f (x) = 7 x, at x = 16

\int \frac{7}{x ^{8}} d x

\frac{1}{4 - x}

x \to 0 + lim (tan^{x} (x))

What is (\partial)/(\partial x)(16sqrt(3x)) ?
The answer to (\partial)/(\partial x)(16sqrt(3x)) is (8sqrt(3))/(sqrt(x))