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)

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derivative of

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

\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}}

x \to 0 lim (e^{x} + e^{- x} - 2)

\int \frac{e ^{x}}{1 - 81 e ^{2 x}} d x

\frac{d}{d x} (- \frac{sin ( x )}{cos ( x )})

y = x^{3} - 2 x + 2, (2, 6)

\frac{d}{d x} (2 \cdot e^{x})

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)