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

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

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

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

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

\frac{2 x ^{5} - 15}{x ^{4}}

Solution steps

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

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

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

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

Simplify

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

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

4 x^{2} + 10, 2 x + 7, - 3, 2

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

\int - \frac{1}{x - 4} d x

4 x - 32 x, at x = 4

\int_{- 1}^{1} x^{4} d x

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