What is the derivative of (3000-10x^2+1)/(3x^3) ?

The derivative of (3000-10x^2+1)/(3x^3) is -(-10x^2+9003)/(3x^4)

What is the first derivative of (3000-10x^2+1)/(3x^3) ?

The first derivative of (3000-10x^2+1)/(3x^3) is -(-10x^2+9003)/(3x^4)

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derivative of

\frac{3000 - 10 x ^{2} + 1}{3 x ^{3}}

- \frac{- 10 x ^{2} + 9003}{3 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{3000 - 10 x ^{2} + 1}{3 x ^{3}})

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (\frac{3000 - 10 x ^{2} + 1}{x ^{3}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( 3000 - 10 x ^{2} + 1 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3000 - 10 x ^{2} + 1 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3000 - 10 x^{2} + 1) = - 20 x

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

= \frac{1}{3} \cdot \frac{( - 20 x ) x ^{3} - 3 x ^{2} ( 3000 - 10 x ^{2} + 1 )}{( x ^{3} ) ^{2}}

Simplify

\frac{1}{3} \cdot \frac{( - 20 x ) x ^{3} - 3 x ^{2} ( 3000 - 10 x ^{2} + 1 )}{( x ^{3} ) ^{2}} : - \frac{- 10 x ^{2} + 9003}{3 x ^{4}}

= - \frac{- 10 x ^{2} + 9003}{3 x ^{4}}

\frac{1}{2} sin (2 t)

\frac{d}{d x} (\frac{1 + x}{1 - x})

7 x - 3

x \to 0 lim (\frac{e ^{x} - 1}{8 x})

\int \frac{2 cos ( x )}{1 + sin ( x )} d x

What is the derivative of (3000-10x^2+1)/(3x^3) ?
The derivative of (3000-10x^2+1)/(3x^3) is -(-10x^2+9003)/(3x^4)
What is the first derivative of (3000-10x^2+1)/(3x^3) ?
The first derivative of (3000-10x^2+1)/(3x^3) is -(-10x^2+9003)/(3x^4)