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 \cdot 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}

\frac{d v}{d t} = 9.81 - \frac{0.5}{v ^{- 1}}

k = 0 \sum \infty 5 \cdot 3^{k}

- \frac{4 x}{( x ^{2} - 1 ) ^{2}}

x \to 0 + lim (x^{2} - 2 x - 3)

\frac{\partial}{\partial x} (2 + y ln (4 + x y^{2}))

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