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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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