What is the derivative of 100x^{3/2} ?

The derivative of 100x^{3/2} is 150x^{1/2}

What is the first derivative of 100x^{3/2} ?

The first derivative of 100x^{3/2} is 150x^{1/2}

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\frac{d}{d x} (100 x^{\frac{3}{2}})

150 x^{\frac{1}{2}}

Solution steps

\frac{d}{d x} (100 x^{\frac{3}{2}})

Take the constant out:

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

= 100 \frac{d}{d x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

= 100 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

100 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : 150 x^{\frac{1}{2}}

= 150 x^{\frac{1}{2}}

What is the derivative of 100x^{3/2} ?
The derivative of 100x^{3/2} is 150x^{1/2}
What is the first derivative of 100x^{3/2} ?
The first derivative of 100x^{3/2} is 150x^{1/2}