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Popular >

derivative of x/(3sqrt(x^2+4))-1/4

Solution

derivative of

\frac{x}{3 x ^{2} + 4} - \frac{1}{4}

Solution

\frac{4}{3 ( x ^{2} + 4 ) x ^{2} + 4}

Solution steps

\frac{d}{d x} (\frac{x}{3 x ^{2} + 4} - \frac{1}{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x}{3 x ^{2} + 4}) - \frac{d}{d x} (\frac{1}{4})

\frac{d}{d x} (\frac{x}{3 x ^{2} + 4}) = \frac{4}{3 ( x ^{2} + 4 ) x ^{2} + 4}

\frac{d}{d x} (\frac{1}{4}) = 0

= \frac{4}{3 ( x ^{2} + 4 ) x ^{2} + 4} - 0

Simplify

= \frac{4}{3 ( x ^{2} + 4 ) x ^{2} + 4}

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

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