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

The derivative of 1+(3/2 x^{(1/2})^2) is 9/4

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

The first derivative of 1+(3/2 x^{(1/2})^2) is 9/4

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

\frac{9}{4}

Decimal

2.25

Solution steps

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

Simplify

1 + (\frac{3}{2} x^{(\frac{1}{2})})^{2} : 1 + \frac{9 x}{4}

= \frac{d}{d x} (1 + \frac{9 x}{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (1) + \frac{d}{d x} (\frac{9 x}{4})

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

\frac{d}{d x} (\frac{9 x}{4}) = \frac{9}{4}

= 0 + \frac{9}{4}

Simplify

= \frac{9}{4}

What is the derivative of 1+(3/2 x^{(1/2})^2) ?
The derivative of 1+(3/2 x^{(1/2})^2) is 9/4
What is the first derivative of 1+(3/2 x^{(1/2})^2) ?
The first derivative of 1+(3/2 x^{(1/2})^2) is 9/4