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

The derivative of (2(x^4-9))/(x^3) is (2(x^4+27))/(x^4)

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

The first derivative of (2(x^4-9))/(x^3) is (2(x^4+27))/(x^4)

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derivative of

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

\frac{2 ( x ^{4} + 27 )}{x ^{4}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

2 \cdot \frac{4 x ^{3} x ^{3} - 3 x ^{2} ( x ^{4} - 9 )}{( x ^{3} ) ^{2}} : \frac{2 ( x ^{4} + 27 )}{x ^{4}}

= \frac{2 ( x ^{4} + 27 )}{x ^{4}}

\frac{d}{d x} (ln (arccos (x) + 2))

\int 4 x^{2} e^{4 x} d x

3 - x

y = x^{8 c o s (x)}

What is the derivative of (2(x^4-9))/(x^3) ?
The derivative of (2(x^4-9))/(x^3) is (2(x^4+27))/(x^4)
What is the first derivative of (2(x^4-9))/(x^3) ?
The first derivative of (2(x^4-9))/(x^3) is (2(x^4+27))/(x^4)