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Popular >

derivative of 1-(3x/(x^3+27))

Solution

\frac{d}{d x} (1 - \frac{3 x}{x ^{3} + 27})

Solution

- \frac{3 ( - 2 x ^{3} + 27 )}{( x ^{3} + 27 ) ^{2}}

Solution steps

\frac{d}{d x} (1 - \frac{3 x}{x ^{3} + 27})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) - \frac{d}{d x} (\frac{3 x}{x ^{3} + 27})

\frac{d}{d x} (1) = 0

\frac{d}{d x} (\frac{3 x}{x ^{3} + 27}) = \frac{3 ( - 2 x ^{3} + 27 )}{( x ^{3} + 27 ) ^{2}}

= 0 - \frac{3 ( - 2 x ^{3} + 27 )}{( x ^{3} + 27 ) ^{2}}

Simplify

= - \frac{3 ( - 2 x ^{3} + 27 )}{( x ^{3} + 27 ) ^{2}}

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\int \frac{2 - t}{t ^{2}} d t

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\int x arctan (2 x) d x

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Frequently Asked Questions (FAQ)

What is the derivative of 1-(3x/(x^3+27)) ?
The derivative of 1-(3x/(x^3+27)) is -(3(-2x^3+27))/((x^3+27)^2)
What is the first derivative of 1-(3x/(x^3+27)) ?
The first derivative of 1-(3x/(x^3+27)) is -(3(-2x^3+27))/((x^3+27)^2)