What is the derivative of 4/x+1/(5x^3+2x) ?

The derivative of 4/x+1/(5x^3+2x) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)

What is the first derivative of 4/x+1/(5x^3+2x) ?

The first derivative of 4/x+1/(5x^3+2x) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)

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derivative of

\frac{4}{x} + \frac{1}{5 x ^{3} + 2 x}

\frac{- 100 x ^{4} - 95 x ^{2} - 18}{x ^{2} ( 5 x ^{2} + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{x} + \frac{1}{5 x ^{3} + 2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (\frac{1}{5 x ^{3} + 2 x})

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

\frac{d}{d x} (\frac{1}{5 x ^{3} + 2 x}) = - \frac{15 x ^{2} + 2}{( 5 x ^{3} + 2 x ) ^{2}}

= - \frac{4}{x ^{2}} - \frac{15 x ^{2} + 2}{( 5 x ^{3} + 2 x ) ^{2}}

Simplify

- \frac{4}{x ^{2}} - \frac{15 x ^{2} + 2}{( 5 x ^{3} + 2 x ) ^{2}} : \frac{- 100 x ^{4} - 95 x ^{2} - 18}{x ^{2} ( 5 x ^{2} + 2 ) ^{2}}

= \frac{- 100 x ^{4} - 95 x ^{2} - 18}{x ^{2} ( 5 x ^{2} + 2 ) ^{2}}

\frac{d}{d t} (4 cos (π t))

(sin (π))^{^{'}}

\frac{d}{d x} (2^{t a n (x)})

\int_{1}^{2} 2 (x - 1) d x

\int \frac{x ^{2}}{4 + x ^{2}} d x

What is the derivative of 4/x+1/(5x^3+2x) ?
The derivative of 4/x+1/(5x^3+2x) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)
What is the first derivative of 4/x+1/(5x^3+2x) ?
The first derivative of 4/x+1/(5x^3+2x) is (-100x^4-95x^2-18)/(x^2(5x^2+2)^2)