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

The derivative of 2x^3+(5x+1/(3x-5)-2/(x^3)) is 6x^2-(28)/((3x-5)^2)+6/(x^4)

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

The first derivative of 2x^3+(5x+1/(3x-5)-2/(x^3)) is 6x^2-(28)/((3x-5)^2)+6/(x^4)

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

6 x^{2} - \frac{28}{( 3 x - 5 ) ^{2}} + \frac{6}{x ^{4}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (\frac{5 x + 1}{3 x - 5}) = - \frac{28}{( 3 x - 5 ) ^{2}}

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

= 6 x^{2} - \frac{28}{( 3 x - 5 ) ^{2}} - (- \frac{6}{x ^{4}})

Simplify

= 6 x^{2} - \frac{28}{( 3 x - 5 ) ^{2}} + \frac{6}{x ^{4}}

y^{^{'}} + y = 8 x e^{x}

\frac{d}{d x} (\frac{1}{12} (x + 2)^{3} + (x + 2)^{- 1})

x \to 0 lim (\frac{7 ^{x} - 9 ^{x}}{x})

g (t) = 4 t^{- \frac{1}{8}}

\int \frac{6}{3 + x ^{2}} d x

What is the derivative of 2x^3+(5x+1/(3x-5)-2/(x^3)) ?
The derivative of 2x^3+(5x+1/(3x-5)-2/(x^3)) is 6x^2-(28)/((3x-5)^2)+6/(x^4)
What is the first derivative of 2x^3+(5x+1/(3x-5)-2/(x^3)) ?
The first derivative of 2x^3+(5x+1/(3x-5)-2/(x^3)) is 6x^2-(28)/((3x-5)^2)+6/(x^4)