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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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