What is the derivative of (x^7+4)/(x^7) ?

The derivative of (x^7+4)/(x^7) is -(28)/(x^8)

What is the first derivative of (x^7+4)/(x^7) ?

The first derivative of (x^7+4)/(x^7) is -(28)/(x^8)

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derivative of

\frac{x ^{7} + 4}{x ^{7}}

- \frac{28}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{x ^{7} + 4}{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} + 4 ) x ^{7} - \frac{d}{d x} ( x ^{7} ) ( x ^{7} + 4 )}{( x ^{7} ) ^{2}}

\frac{d}{d x} (x^{7} + 4) = 7 x^{6}

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

= \frac{7 x ^{6} x ^{7} - 7 x ^{6} ( x ^{7} + 4 )}{( x ^{7} ) ^{2}}

Simplify

\frac{7 x ^{6} x ^{7} - 7 x ^{6} ( x ^{7} + 4 )}{( x ^{7} ) ^{2}} : - \frac{28}{x ^{8}}

= - \frac{28}{x ^{8}}

y = 10 cos (x), (\frac{π}{3}, 5)

\frac{d y}{d x} = \frac{( 5 x sec ( \frac{y}{x} ) + y )}{x}

\frac{\partial}{\partial x} (x sin (x + y^{2}))

\frac{d}{d x} (\frac{5 x}{x - 1})

\int_{1}^{6} t ln (t) d t

What is the derivative of (x^7+4)/(x^7) ?
The derivative of (x^7+4)/(x^7) is -(28)/(x^8)
What is the first derivative of (x^7+4)/(x^7) ?
The first derivative of (x^7+4)/(x^7) is -(28)/(x^8)