What is the derivative of 12sqrt(t) ?

The derivative of 12sqrt(t) is 6/(sqrt(t))

What is the first derivative of 12sqrt(t) ?

The first derivative of 12sqrt(t) is 6/(sqrt(t))

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derivative of

12 t

\frac{6}{t}

Solution steps

\frac{d}{d t} (12 t)

Take the constant out:

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

= 12 \frac{d}{d t} (t)

Apply radical rule:

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

= 12 \frac{d}{d t} (t^{\frac{1}{2}})

Apply the Power Rule:

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

= 12 \cdot \frac{1}{2} t^{\frac{1}{2} - 1}

Simplify

12 \cdot \frac{1}{2} t^{\frac{1}{2} - 1} : \frac{6}{t}

= \frac{6}{t}

What is the derivative of 12sqrt(t) ?
The derivative of 12sqrt(t) is 6/(sqrt(t))
What is the first derivative of 12sqrt(t) ?
The first derivative of 12sqrt(t) is 6/(sqrt(t))