What is the derivative of x^7(1-2/(x+4)) ?

The derivative of x^7(1-2/(x+4)) is (7x^8+44x^7+56x^6)/((x+4)^2)

What is the first derivative of x^7(1-2/(x+4)) ?

The first derivative of x^7(1-2/(x+4)) is (7x^8+44x^7+56x^6)/((x+4)^2)

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derivative of

x^{7} (1 - \frac{2}{x + 4})

\frac{7 x ^{8} + 44 x ^{7} + 56 x ^{6}}{( x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (x^{7} (1 - \frac{2}{x + 4}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{7}, g = 1 - \frac{2}{x + 4}

= \frac{d}{d x} (x^{7}) (1 - \frac{2}{x + 4}) + \frac{d}{d x} (1 - \frac{2}{x + 4}) x^{7}

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

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

= 7 x^{6} (1 - \frac{2}{x + 4}) + \frac{2}{( x + 4 ) ^{2}} x^{7}

Simplify

7 x^{6} (1 - \frac{2}{x + 4}) + \frac{2}{( x + 4 ) ^{2}} x^{7} : \frac{7 x ^{8} + 44 x ^{7} + 56 x ^{6}}{( x + 4 ) ^{2}}

= \frac{7 x ^{8} + 44 x ^{7} + 56 x ^{6}}{( x + 4 ) ^{2}}

What is the derivative of x^7(1-2/(x+4)) ?
The derivative of x^7(1-2/(x+4)) is (7x^8+44x^7+56x^6)/((x+4)^2)
What is the first derivative of x^7(1-2/(x+4)) ?
The first derivative of x^7(1-2/(x+4)) is (7x^8+44x^7+56x^6)/((x+4)^2)