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

The derivative of ((2x^2+1^4)/2) is 8x(2x^2+1)^3

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

The first derivative of ((2x^2+1^4)/2) is 8x(2x^2+1)^3

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

8 x (2 x^{2} + 1)^{3}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2} \cdot 4 (2 x^{2} + 1)^{3} \cdot 4 x : 8 x (2 x^{2} + 1)^{3}

= 8 x (2 x^{2} + 1)^{3}

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What is the derivative of ((2x^2+1^4)/2) ?
The derivative of ((2x^2+1^4)/2) is 8x(2x^2+1)^3
What is the first derivative of ((2x^2+1^4)/2) ?
The first derivative of ((2x^2+1^4)/2) is 8x(2x^2+1)^3