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

The derivative of (x^6/(5-x^5)) is (30x^5-x^{10})/((5-x^5)^2)

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

The first derivative of (x^6/(5-x^5)) is (30x^5-x^{10})/((5-x^5)^2)

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

\frac{30 x ^{5} - x ^{10}}{( 5 - x ^{5} ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{6 x ^{5} ( 5 - x ^{5} ) - ( - 5 x ^{4} ) x ^{6}}{( 5 - x ^{5} ) ^{2}} : \frac{30 x ^{5} - x ^{10}}{( 5 - x ^{5} ) ^{2}}

= \frac{30 x ^{5} - x ^{10}}{( 5 - x ^{5} ) ^{2}}

x = 9 y^{2}, x = 20 + 4 y^{2}

x \to \infty lim (e)

\int_{0}^{1} (x + 6) (x - 7) d x

What is the derivative of (x^6/(5-x^5)) ?
The derivative of (x^6/(5-x^5)) is (30x^5-x^{10})/((5-x^5)^2)
What is the first derivative of (x^6/(5-x^5)) ?
The first derivative of (x^6/(5-x^5)) is (30x^5-x^{10})/((5-x^5)^2)