What is the derivative of y=((x^7-4x^3+12x))/(x^3) ?

The derivative of y=((x^7-4x^3+12x))/(x^3) is (4(x^6-6))/(x^3)

What is the first derivative of y=((x^7-4x^3+12x))/(x^3) ?

The first derivative of y=((x^7-4x^3+12x))/(x^3) is (4(x^6-6))/(x^3)

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derivative of

y = \frac{( x ^{7} - 4 x ^{3} + 12 x )}{x ^{3}}

\frac{4 ( x ^{6} - 6 )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{7} - 4 x ^{3} + 12 x}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{7} - 4 x ^{3} + 12 x ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( x ^{7} - 4 x ^{3} + 12 x )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (x^{7} - 4 x^{3} + 12 x) = 7 x^{6} - 12 x^{2} + 12

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

= \frac{( 7 x ^{6} - 12 x ^{2} + 12 ) x ^{3} - 3 x ^{2} ( x ^{7} - 4 x ^{3} + 12 x )}{( x ^{3} ) ^{2}}

Simplify

\frac{( 7 x ^{6} - 12 x ^{2} + 12 ) x ^{3} - 3 x ^{2} ( x ^{7} - 4 x ^{3} + 12 x )}{( x ^{3} ) ^{2}} : \frac{4 ( x ^{6} - 6 )}{x ^{3}}

= \frac{4 ( x ^{6} - 6 )}{x ^{3}}

What is the derivative of y=((x^7-4x^3+12x))/(x^3) ?
The derivative of y=((x^7-4x^3+12x))/(x^3) is (4(x^6-6))/(x^3)
What is the first derivative of y=((x^7-4x^3+12x))/(x^3) ?
The first derivative of y=((x^7-4x^3+12x))/(x^3) is (4(x^6-6))/(x^3)