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

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

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

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

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

\frac{4 x ^{5} - 15}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (2 x^{5} + 5) = 10 x^{4}

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

= \frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 5 )}{( x ^{3} ) ^{2}}

Simplify

\frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 5 )}{( x ^{3} ) ^{2}} : \frac{4 x ^{5} - 15}{x ^{4}}

= \frac{4 x ^{5} - 15}{x ^{4}}

\frac{1}{2 r} + \frac{1}{5 r ^{\frac{4}{5}}}

\int \frac{- x}{1 - 0.5 x} d x

\frac{\partial}{\partial x} (2 x^{2} - 4 x y + y^{4})

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

sin^{2} (x^{2})

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