What is the derivative of y=(2x^5+8)/(x^3) ?

The derivative of y=(2x^5+8)/(x^3) is (4(x^5-6))/(x^4)

What is the first derivative of y=(2x^5+8)/(x^3) ?

The first derivative of y=(2x^5+8)/(x^3) is (4(x^5-6))/(x^4)

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derivative of

y = \frac{2 x ^{5} + 8}{x ^{3}}

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

Solution steps

\frac{d}{d x} (\frac{2 x ^{5} + 8}{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} + 8 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (2 x^{5} + 8) = 10 x^{4}

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

= \frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}}

Simplify

\frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}} : \frac{4 ( x ^{5} - 6 )}{x ^{4}}

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

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

x \to \infty lim (\frac{e ^{2 x}}{e ^{2 x} + 1})

\int \frac{1}{1 + 21 x} d x

f (x) = e^{8}

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

What is the derivative of y=(2x^5+8)/(x^3) ?
The derivative of y=(2x^5+8)/(x^3) is (4(x^5-6))/(x^4)
What is the first derivative of y=(2x^5+8)/(x^3) ?
The first derivative of y=(2x^5+8)/(x^3) is (4(x^5-6))/(x^4)