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Popular Calculus >

derivative of ((x^6+1))/(x^5)

Solution

derivative of

\frac{( x ^{6} + 1 )}{x ^{5}}

Solution

\frac{x ^{6} - 5}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{x ^{6} + 1}{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} + 1 ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( x ^{6} + 1 )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (x^{6} + 1) = 6 x^{5}

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

= \frac{6 x ^{5} x ^{5} - 5 x ^{4} ( x ^{6} + 1 )}{( x ^{5} ) ^{2}}

Simplify

\frac{6 x ^{5} x ^{5} - 5 x ^{4} ( x ^{6} + 1 )}{( x ^{5} ) ^{2}} : \frac{x ^{6} - 5}{x ^{6}}

= \frac{x ^{6} - 5}{x ^{6}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ((x^6+1))/(x^5) ?
The derivative of ((x^6+1))/(x^5) is (x^6-5)/(x^6)
What is the first derivative of ((x^6+1))/(x^5) ?
The first derivative of ((x^6+1))/(x^5) is (x^6-5)/(x^6)