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

The derivative of (5x^3/4-2/(5x^3)) is (15x^2)/4+6/(5x^4)

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

The first derivative of (5x^3/4-2/(5x^3)) is (15x^2)/4+6/(5x^4)

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

\frac{15 x ^{2}}{4} + \frac{6}{5 x ^{4}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{15 x ^{2}}{4} - (- \frac{6}{5 x ^{4}})

Simplify

= \frac{15 x ^{2}}{4} + \frac{6}{5 x ^{4}}

What is the derivative of (5x^3/4-2/(5x^3)) ?
The derivative of (5x^3/4-2/(5x^3)) is (15x^2)/4+6/(5x^4)
What is the first derivative of (5x^3/4-2/(5x^3)) ?
The first derivative of (5x^3/4-2/(5x^3)) is (15x^2)/4+6/(5x^4)