What is the derivative of (21x^{1/2}/2) ?

The derivative of (21x^{1/2}/2) is (21)/(4x^{1/2)}

What is the first derivative of (21x^{1/2}/2) ?

The first derivative of (21x^{1/2}/2) is (21)/(4x^{1/2)}

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\frac{d}{d x} (\frac{21 x ^{\frac{1}{2}}}{2})

\frac{21}{4 x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (\frac{21 x ^{\frac{1}{2}}}{2})

Take the constant out:

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

= \frac{21}{2} \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= \frac{21}{2} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

\frac{21}{2} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{21}{4 x ^{\frac{1}{2}}}

= \frac{21}{4 x ^{\frac{1}{2}}}

\int_{- 2}^{3} (x^{2} - x - 6) d x

\int sin (3 t - 3 x) d x

y = \frac{1}{5 + 3 x}, (1, \frac{1}{8})

y = 5 x - 3

y = 7 + 5 x^{2} - 2 x^{3}

What is the derivative of (21x^{1/2}/2) ?
The derivative of (21x^{1/2}/2) is (21)/(4x^{1/2)}
What is the first derivative of (21x^{1/2}/2) ?
The first derivative of (21x^{1/2}/2) is (21)/(4x^{1/2)}