What is the derivative of sqrt(x^4-3x^2+4) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{4} - 3 x^{2} + 4) = 4 x^{3} - 6 x

= \frac{1}{2 x ^{4} - 3 x ^{2} + 4} (4 x^{3} - 6 x)

Simplify

\frac{1}{2 x ^{4} - 3 x ^{2} + 4} (4 x^{3} - 6 x) : \frac{x ( 2 x ^{2} - 3 )}{x ^{4} - 3 x ^{2} + 4}

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

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