What is the derivative of 2pi(x/(9.8)^{1/2}) ?

The derivative of 2pi(x/(9.8)^{1/2}) is (1.00354…)/(x^{1/2)}

What is the first derivative of 2pi(x/(9.8)^{1/2}) ?

The first derivative of 2pi(x/(9.8)^{1/2}) is (1.00354…)/(x^{1/2)}

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\frac{d}{d x} (2 π (\frac{x}{9.8})^{\frac{1}{2}})

\frac{1.00354 \dots}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (2 π (\frac{x}{9.8})^{\frac{1}{2}})

Simplify

2 π (\frac{x}{9.8})^{\frac{1}{2}} : 2.00708 \dots x^{\frac{1}{2}}

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

Take the constant out:

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

= 2.00708 \dots \frac{d}{d x} (x^{\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} x^{\frac{1}{2} - 1}

Simplify

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

= \frac{1.00354 \dots}{x ^{\frac{1}{2}}}

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What is the derivative of 2pi(x/(9.8)^{1/2}) ?
The derivative of 2pi(x/(9.8)^{1/2}) is (1.00354…)/(x^{1/2)}
What is the first derivative of 2pi(x/(9.8)^{1/2}) ?
The first derivative of 2pi(x/(9.8)^{1/2}) is (1.00354…)/(x^{1/2)}