What is the derivative of (3x^5+9/(x^3)) ?

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

What is the first derivative of (3x^5+9/(x^3)) ?

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

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\frac{d}{d x} (\frac{3 x ^{5} + 9}{x ^{3}})

\frac{3 ( 2 x ^{5} - 9 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{5} + 9}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ^{5} + 9 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3 x ^{5} + 9 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3 x^{5} + 9) = 15 x^{4}

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

= \frac{15 x ^{4} x ^{3} - 3 x ^{2} ( 3 x ^{5} + 9 )}{( x ^{3} ) ^{2}}

Simplify

\frac{15 x ^{4} x ^{3} - 3 x ^{2} ( 3 x ^{5} + 9 )}{( x ^{3} ) ^{2}} : \frac{3 ( 2 x ^{5} - 9 )}{x ^{4}}

= \frac{3 ( 2 x ^{5} - 9 )}{x ^{4}}

\int \frac{1}{8 x + 1} d x

x \to 1 + lim (ln (x - 1))

\int e^{4 x + 7} d x

e^{x} \cdot sin (2 x)

f (t) = t^{2} + 6 t - 3

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