What is the d/(dl)(2pisqrt(l/(9.8))) ?

The d/(dl)(2pisqrt(l/(9.8))) is (1.00354…)/(sqrt(l))

What is the first d/(dl)(2pisqrt(l/(9.8))) ?

The first d/(dl)(2pisqrt(l/(9.8))) is (1.00354…)/(sqrt(l))

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\frac{d}{d l} (2 π \frac{l}{9.8})

\frac{1.00354 \dots}{l}

Solution steps

\frac{d}{d l} (2 π \frac{l}{9.8})

Simplify

2 π \frac{l}{9.8} : 2.00708 \dots l

= \frac{d}{d l} (2.00708 \dots l)

Take the constant out:

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

= 2.00708 \dots \frac{d}{d l} (l)

Apply radical rule:

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

= 2.00708 \dots \frac{d}{d l} (l^{\frac{1}{2}})

Apply the Power Rule:

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

= 2.00708 \dots \cdot \frac{1}{2} l^{\frac{1}{2} - 1}

Simplify

2.00708 \dots \cdot \frac{1}{2} l^{\frac{1}{2} - 1} : \frac{1.00354 \dots}{l}

= \frac{1.00354 \dots}{l}

What is the d/(dl)(2pisqrt(l/(9.8))) ?
The d/(dl)(2pisqrt(l/(9.8))) is (1.00354…)/(sqrt(l))
What is the first d/(dl)(2pisqrt(l/(9.8))) ?
The first d/(dl)(2pisqrt(l/(9.8))) is (1.00354…)/(sqrt(l))