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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derivative of

\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}}

\int \frac{1}{25 x ^{2} - 4} d x

\frac{\partial}{\partial y} (e^{x} sin (y) + 3 y)

\int \frac{1}{x ^{2} + 3 x - 4} d x

\int \frac{x ^{2} + 1}{x ^{3}} d x

x \to 0 lim (4 - 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)