What is the derivative of h(sqrt(x)) ?

The derivative of h(sqrt(x)) is h/(2sqrt(x))

What is the first derivative of h(sqrt(x)) ?

The first derivative of h(sqrt(x)) is h/(2sqrt(x))

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\frac{d}{d x} (h (x))

\frac{h}{2 x}

Solution steps

\frac{d}{d x} (h (x))

Treat

h

as a constant

Take the constant out:

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

= h \frac{d}{d x} (x)

Apply radical rule:

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

= h \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

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

Simplify

h \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{h}{2 x}

= \frac{h}{2 x}

f (x) = \frac{9}{x}

\frac{d y}{d x} = \frac{1}{6} y cos^{2} (y)

\int 11 (tan (x)) (ln (cos (x))) d x

\frac{\frac{1}{7}}{s ^{2} + \frac{19980}{7}}

\int t^{- \frac{1}{2}} (t^{4} + 2 t^{2} - 1) d t

What is the derivative of h(sqrt(x)) ?
The derivative of h(sqrt(x)) is h/(2sqrt(x))
What is the first derivative of h(sqrt(x)) ?
The first derivative of h(sqrt(x)) is h/(2sqrt(x))