What is the derivative of ((x^2-4^{3/2})/6) ?

The derivative of ((x^2-4^{3/2})/6) is (x(x^2-4)^{1/2})/2

What is the first derivative of ((x^2-4^{3/2})/6) ?

The first derivative of ((x^2-4^{3/2})/6) is (x(x^2-4)^{1/2})/2

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

n = 0 \sum \infty π

x \to \infty lim (1 - \frac{5}{x})

x \to 3 lim (5 x)

n = 0 \sum \infty (- 1)^{n} n

\int \frac{1}{( 1 - 6 x ) ^{\frac{7}{2}}} d x

What is the derivative of ((x^2-4^{3/2})/6) ?
The derivative of ((x^2-4^{3/2})/6) is (x(x^2-4)^{1/2})/2
What is the first derivative of ((x^2-4^{3/2})/6) ?
The first derivative of ((x^2-4^{3/2})/6) is (x(x^2-4)^{1/2})/2