What is the derivative of f(x)=sqrt(8-x^3) ?

The derivative of f(x)=sqrt(8-x^3) is -(3x^2)/(2sqrt(8-x^3))

What is the first derivative of f(x)=sqrt(8-x^3) ?

The first derivative of f(x)=sqrt(8-x^3) is -(3x^2)/(2sqrt(8-x^3))

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derivative

- \frac{3 x ^{2}}{2 8 - x ^{3}}

Solution steps

\frac{d}{d x} (8 - x^{3})

Apply the chain rule:

\frac{1}{2 8 - x ^{3}} \frac{d}{d x} (8 - x^{3})

= \frac{1}{2 8 - x ^{3}} \frac{d}{d x} (8 - x^{3})

\frac{d}{d x} (8 - x^{3}) = - 3 x^{2}

= \frac{1}{2 8 - x ^{3}} (- 3 x^{2})

Simplify

\frac{1}{2 8 - x ^{3}} (- 3 x^{2}) : - \frac{3 x ^{2}}{2 8 - x ^{3}}

= - \frac{3 x ^{2}}{2 8 - x ^{3}}

What is the derivative of f(x)=sqrt(8-x^3) ?
The derivative of f(x)=sqrt(8-x^3) is -(3x^2)/(2sqrt(8-x^3))
What is the first derivative of f(x)=sqrt(8-x^3) ?
The first derivative of f(x)=sqrt(8-x^3) is -(3x^2)/(2sqrt(8-x^3))