What is the d/(dt)(sqrt(t)) ?

The d/(dt)(sqrt(t)) is 1/(2sqrt(t))

What is the first d/(dt)(sqrt(t)) ?

The first d/(dt)(sqrt(t)) is 1/(2sqrt(t))

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\frac{d}{d t} (t)

\frac{1}{2 t}

Solution steps

\frac{d}{d t} (t)

Apply radical rule:

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

= \frac{d}{d t} (t^{\frac{1}{2}})

Apply the Power Rule:

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

= \frac{1}{2} t^{\frac{1}{2} - 1}

Simplify

\frac{1}{2} t^{\frac{1}{2} - 1} : \frac{1}{2 t}

= \frac{1}{2 t}

x y^{^{'}} - 4 y = x

f (t) = cos (t)

x \to 0 lim ((1 + 7 x)^{\frac{2}{x}})

\frac{\partial}{\partial x} (x^{2} y^{3} + 4 x yz - 3 yz)

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