What is the derivative of x^2sqrt(x^4-12) ?

The derivative of x^2sqrt(x^4-12) is (4x^5-24x)/(sqrt(x^4-12))

What is the first derivative of x^2sqrt(x^4-12) ?

The first derivative of x^2sqrt(x^4-12) is (4x^5-24x)/(sqrt(x^4-12))

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\frac{d}{d x} (x^{2} x^{4} - 12)

\frac{4 x ^{5} - 24 x}{x ^{4} - 12}

Solution steps

\frac{d}{d x} (x^{2} x^{4} - 12)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = x^{4} - 12

= \frac{d}{d x} (x^{2}) x^{4} - 12 + \frac{d}{d x} (x^{4} - 12) x^{2}

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

\frac{d}{d x} (x^{4} - 12) = \frac{2 x ^{3}}{x ^{4} - 12}

= 2 x x^{4} - 12 + \frac{2 x ^{3}}{x ^{4} - 12} x^{2}

Simplify

2 x x^{4} - 12 + \frac{2 x ^{3}}{x ^{4} - 12} x^{2} : \frac{4 x ^{5} - 24 x}{x ^{4} - 12}

= \frac{4 x ^{5} - 24 x}{x ^{4} - 12}

\frac{d y}{d x} = \frac{( 3 x ^{2} )}{y ^{2}}

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

x \to - 2 lim (x (2))

\frac{\partial}{\partial y} (2 e^{x})

\frac{d}{d t} (sec (t) tan (t))

What is the derivative of x^2sqrt(x^4-12) ?
The derivative of x^2sqrt(x^4-12) is (4x^5-24x)/(sqrt(x^4-12))
What is the first derivative of x^2sqrt(x^4-12) ?
The first derivative of x^2sqrt(x^4-12) is (4x^5-24x)/(sqrt(x^4-12))