What is (\partial)/(\partial x)(sqrt(x)ln(t)) ?

The answer to (\partial)/(\partial x)(sqrt(x)ln(t)) is (ln(t))/(2sqrt(x))

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(\partial)/(\partial x)(sqrt(x)ln(t))

\frac{\partial}{\partial x} (x ln (t))

\frac{ln ( t )}{2 x}

Solution steps

\frac{\partial}{\partial x} (x ln (t))

Treat

t

as a constant

Take the constant out:

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

= ln (t) \frac{\partial}{\partial x} (x)

Apply radical rule:

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

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

Apply the Power Rule:

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

= ln (t) \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

ln (t) \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{ln ( t )}{2 x}

= \frac{ln ( t )}{2 x}

5 y^{^{'}} - 15 x^{2} = 0

n \to 10 lim ([1 + (\frac{1}{n})]^{n})

n = 0 \sum \infty (\frac{i}{3})^{n}

\frac{d}{d x} (2 (1 - x)^{- 3})

x \to 0 lim (\frac{5 ^{x} - 4 ^{x}}{x})

What is (\partial)/(\partial x)(sqrt(x)ln(t)) ?
The answer to (\partial)/(\partial x)(sqrt(x)ln(t)) is (ln(t))/(2sqrt(x))