What is the derivative of 7sqrt(t) ?

The derivative of 7sqrt(t) is 7/(2sqrt(t))

What is the first derivative of 7sqrt(t) ?

The first derivative of 7sqrt(t) is 7/(2sqrt(t))

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derivative of

7 t

\frac{7}{2 t}

Solution steps

\frac{d}{d t} (7 t)

Take the constant out:

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

= 7 \frac{d}{d t} (t)

Apply radical rule:

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

= 7 \frac{d}{d t} (t^{\frac{1}{2}})

Apply the Power Rule:

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

= 7 \cdot \frac{1}{2} t^{\frac{1}{2} - 1}

Simplify

7 \cdot \frac{1}{2} t^{\frac{1}{2} - 1} : \frac{7}{2 t}

= \frac{7}{2 t}

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What is the derivative of 7sqrt(t) ?
The derivative of 7sqrt(t) is 7/(2sqrt(t))
What is the first derivative of 7sqrt(t) ?
The first derivative of 7sqrt(t) is 7/(2sqrt(t))