What is the derivative of f(x)=xsqrt(x^3-6) ?

The derivative of f(x)=xsqrt(x^3-6) is (5x^3-12)/(2sqrt(x^3-6))

What is the first derivative of f(x)=xsqrt(x^3-6) ?

The first derivative of f(x)=xsqrt(x^3-6) is (5x^3-12)/(2sqrt(x^3-6))

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derivative of

f (x) = x x^{3} - 6

\frac{5 x ^{3} - 12}{2 x ^{3} - 6}

Solution steps

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

Apply the Product Rule:

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

f = x, g = x^{3} - 6

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

\frac{d x}{d x} = 1

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

= 1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x

Simplify

1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x : \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

= \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

What is the derivative of f(x)=xsqrt(x^3-6) ?
The derivative of f(x)=xsqrt(x^3-6) is (5x^3-12)/(2sqrt(x^3-6))
What is the first derivative of f(x)=xsqrt(x^3-6) ?
The first derivative of f(x)=xsqrt(x^3-6) is (5x^3-12)/(2sqrt(x^3-6))