What is the derivative of sqrt(1+x^{256)}-1 ?

The derivative of sqrt(1+x^{256)}-1 is (128x^{255})/(sqrt(x^{256)+1)}

What is the first derivative of sqrt(1+x^{256)}-1 ?

The first derivative of sqrt(1+x^{256)}-1 is (128x^{255})/(sqrt(x^{256)+1)}

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\frac{d}{d x} (1 + x^{256} - 1)

\frac{128 x ^{255}}{x ^{256} + 1}

Solution steps

\frac{d}{d x} (1 + x^{256} - 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (1 + x^{256}) - \frac{d}{d x} (1)

\frac{d}{d x} (1 + x^{256}) = \frac{128 x ^{255}}{1 + x ^{256}}

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

= \frac{128 x ^{255}}{1 + x ^{256}} - 0

Simplify

= \frac{128 x ^{255}}{x ^{256} + 1}

What is the derivative of sqrt(1+x^{256)}-1 ?
The derivative of sqrt(1+x^{256)}-1 is (128x^{255})/(sqrt(x^{256)+1)}
What is the first derivative of sqrt(1+x^{256)}-1 ?
The first derivative of sqrt(1+x^{256)}-1 is (128x^{255})/(sqrt(x^{256)+1)}