What is the derivative of (sqrt(5x^4+x^2)/2) ?

The derivative of (sqrt(5x^4+x^2)/2) is (10x^2+1)/(2sqrt(5x^2+1))

What is the first derivative of (sqrt(5x^4+x^2)/2) ?

The first derivative of (sqrt(5x^4+x^2)/2) is (10x^2+1)/(2sqrt(5x^2+1))

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\frac{d}{d x} (\frac{5 x ^{4} + x ^{2}}{2})

\frac{10 x ^{2} + 1}{2 5 x ^{2} + 1}

Solution steps

\frac{d}{d x} (\frac{5 x ^{4} + x ^{2}}{2})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (5 x^{4} + x^{2})

Apply the chain rule:

\frac{1}{2 5 x ^{4} + x ^{2}} \frac{d}{d x} (5 x^{4} + x^{2})

= \frac{1}{2 5 x ^{4} + x ^{2}} \frac{d}{d x} (5 x^{4} + x^{2})

\frac{d}{d x} (5 x^{4} + x^{2}) = 20 x^{3} + 2 x

= \frac{1}{2} \cdot \frac{1}{2 5 x ^{4} + x ^{2}} (20 x^{3} + 2 x)

Simplify

\frac{1}{2} \cdot \frac{1}{2 5 x ^{4} + x ^{2}} (20 x^{3} + 2 x) : \frac{10 x ^{2} + 1}{2 5 x ^{2} + 1}

= \frac{10 x ^{2} + 1}{2 5 x ^{2} + 1}

What is the derivative of (sqrt(5x^4+x^2)/2) ?
The derivative of (sqrt(5x^4+x^2)/2) is (10x^2+1)/(2sqrt(5x^2+1))
What is the first derivative of (sqrt(5x^4+x^2)/2) ?
The first derivative of (sqrt(5x^4+x^2)/2) is (10x^2+1)/(2sqrt(5x^2+1))