What is the derivative of x^{3/2}-1 ?

The derivative of x^{3/2}-1 is (3x^{1/2})/2

What is the first derivative of x^{3/2}-1 ?

The first derivative of x^{3/2}-1 is (3x^{1/2})/2

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\frac{d}{d x} (x^{\frac{3}{2}} - 1)

\frac{3 x ^{\frac{1}{2}}}{2}

Solution steps

\frac{d}{d x} (x^{\frac{3}{2}} - 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{\frac{3}{2}}) - \frac{d}{d x} (1)

\frac{d}{d x} (x^{\frac{3}{2}}) = \frac{3 x ^{\frac{1}{2}}}{2}

\frac{d}{d x} (1) = 0

= \frac{3 x ^{\frac{1}{2}}}{2} - 0

Simplify

= \frac{3 x ^{\frac{1}{2}}}{2}

What is the derivative of x^{3/2}-1 ?
The derivative of x^{3/2}-1 is (3x^{1/2})/2
What is the first derivative of x^{3/2}-1 ?
The first derivative of x^{3/2}-1 is (3x^{1/2})/2