What is the derivative of (4x^5+6/(x^3)) ?

The derivative of (4x^5+6/(x^3)) is (2(4x^5-9))/(x^4)

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

The first derivative of (4x^5+6/(x^3)) is (2(4x^5-9))/(x^4)

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\frac{d}{d x} (\frac{4 x ^{5} + 6}{x ^{3}})

\frac{2 ( 4 x ^{5} - 9 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{5} + 6}{x ^{3}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x^{5} + 6) = 20 x^{4}

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

= \frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 6 )}{( x ^{3} ) ^{2}}

Simplify

\frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 6 )}{( x ^{3} ) ^{2}} : \frac{2 ( 4 x ^{5} - 9 )}{x ^{4}}

= \frac{2 ( 4 x ^{5} - 9 )}{x ^{4}}

- \frac{5}{x}

x, x^{2}, [0, 1]

x \to \infty lim (x \cdot 3)

x + y = 5

\int 2 sin (x) - cos (x) d x

What is the derivative of (4x^5+6/(x^3)) ?
The derivative of (4x^5+6/(x^3)) is (2(4x^5-9))/(x^4)
What is the first derivative of (4x^5+6/(x^3)) ?
The first derivative of (4x^5+6/(x^3)) is (2(4x^5-9))/(x^4)