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

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

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

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

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derivative of

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

3 x (x^{2} + 2)^{2}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 3 x (x^{2} + 2)^{2}

\frac{- 2 x}{cos ( x )}

\frac{d}{d t} (3 cos^{6} (t))

e^{3} x + 2

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

3 x^{5} + 25 x^{2} - 8 x + 11

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