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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{11 x e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

(1 - x)^{- 2}

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

\int_{- 2}^{1} \frac{x ^{2} + 4 x + 8}{x - 2} d x

g (x) = cos (x) + 1, f (x) = sin (x)

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