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Popular >

derivative of f(x)=sqrt(8-x^3)

Solution

derivative of

f (x) = 8 - x^{3}

Solution

- \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}}

Popular Examples

slope of x+y=3 slope

x + y = 3

tangent of f(x)=7x^2+2x-7,\at x=-3 tangent of

f (x) = 7 x^{2} + 2 x - 7, at x = - 3

slope of-3x+5y=2x+3y slope

- 3 x + 5 y = 2 x + 3 y

cartesian (4,-(2pi)/3)polar to cartesian

(4, - \frac{2 π}{3})

cartesian (-sqrt(2),(5pi)/4)polar to cartesian

(- 2, \frac{5 π}{4})

Frequently Asked Questions (FAQ)

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))