What is the derivative of (x^6/(2-x^5)) ?

The derivative of (x^6/(2-x^5)) is (12x^5-x^{10})/((2-x^5)^2)

What is the first derivative of (x^6/(2-x^5)) ?

The first derivative of (x^6/(2-x^5)) is (12x^5-x^{10})/((2-x^5)^2)

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\frac{d}{d x} (\frac{x ^{6}}{2 - x ^{5}})

\frac{12 x ^{5} - x ^{10}}{( 2 - x ^{5} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{6}}{2 - x ^{5}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{6 x ^{5} ( 2 - x ^{5} ) - ( - 5 x ^{4} ) x ^{6}}{( 2 - x ^{5} ) ^{2}} : \frac{12 x ^{5} - x ^{10}}{( 2 - x ^{5} ) ^{2}}

= \frac{12 x ^{5} - x ^{10}}{( 2 - x ^{5} ) ^{2}}

What is the derivative of (x^6/(2-x^5)) ?
The derivative of (x^6/(2-x^5)) is (12x^5-x^{10})/((2-x^5)^2)
What is the first derivative of (x^6/(2-x^5)) ?
The first derivative of (x^6/(2-x^5)) is (12x^5-x^{10})/((2-x^5)^2)