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Popular >

derivative of (x^7+2)/(x^7)

Solution

derivative of

\frac{x ^{7} + 2}{x ^{7}}

Solution

- \frac{14}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{x ^{7} + 2}{x ^{7}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{7} + 2 ) x ^{7} - \frac{d}{d x} ( x ^{7} ) ( x ^{7} + 2 )}{( x ^{7} ) ^{2}}

\frac{d}{d x} (x^{7} + 2) = 7 x^{6}

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{7 x ^{6} x ^{7} - 7 x ^{6} ( x ^{7} + 2 )}{( x ^{7} ) ^{2}}

Simplify

\frac{7 x ^{6} x ^{7} - 7 x ^{6} ( x ^{7} + 2 )}{( x ^{7} ) ^{2}} : - \frac{14}{x ^{8}}

= - \frac{14}{x ^{8}}

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\frac{d y}{d x} = - \frac{4 x + 4 y}{4 x + 9 y}

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x \to 2 + lim (\frac{x - 3}{x ^{2} - 4})

Frequently Asked Questions (FAQ)

What is the derivative of (x^7+2)/(x^7) ?
The derivative of (x^7+2)/(x^7) is -(14)/(x^8)
What is the first derivative of (x^7+2)/(x^7) ?
The first derivative of (x^7+2)/(x^7) is -(14)/(x^8)