What is the d/(dθ)(sqrt(θ)) ?

The d/(dθ)(sqrt(θ)) is 1/(2sqrt(θ))

What is the first d/(dθ)(sqrt(θ)) ?

The first d/(dθ)(sqrt(θ)) is 1/(2sqrt(θ))

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\frac{d}{d θ} (θ)

\frac{1}{2 θ}

Solution steps

\frac{d}{d θ} (θ)

Apply radical rule:

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

= \frac{d}{d θ} (θ^{\frac{1}{2}})

Apply the Power Rule:

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

= \frac{1}{2} θ^{\frac{1}{2} - 1}

Simplify

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

= \frac{1}{2 θ}

\int sin (7 x) cos (7 x) d x

\frac{\partial}{\partial x} (\frac{x - y}{2 x y + 5})

(sin (x))^{x}

\int 30 x^{5} d x

x^{3} - 2 x + 2 (4.58)