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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (sin^{2} (2 x))

y = - x^{2} + 62

\frac{d}{d x} (\frac{cos ( x )}{cos ( x ) + 1})

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

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