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

The derivative of x^6(1-1/(x+5)) is (6x^7+55x^6+120x^5)/((x+5)^2)

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

The first derivative of x^6(1-1/(x+5)) is (6x^7+55x^6+120x^5)/((x+5)^2)

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derivative of

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

\frac{6 x ^{7} + 55 x ^{6} + 120 x ^{5}}{( x + 5 ) ^{2}}

Solution steps

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

Apply the Product Rule:

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

f = x^{6}, g = 1 - \frac{1}{x + 5}

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

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

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

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

Simplify

6 x^{5} (1 - \frac{1}{x + 5}) + \frac{1}{( x + 5 ) ^{2}} x^{6} : \frac{6 x ^{7} + 55 x ^{6} + 120 x ^{5}}{( x + 5 ) ^{2}}

= \frac{6 x ^{7} + 55 x ^{6} + 120 x ^{5}}{( x + 5 ) ^{2}}

\int_{1}^{8} \frac{7 ln ( x )}{x ^{2}} d x

x \to 2 lim (\frac{1}{x} - \frac{1}{x ^{2}})

\frac{π}{6}

\int \frac{x - 2}{x ^{3} - x ^{2}} d x

\frac{d}{d x} (co tan (x))

What is the derivative of x^6(1-1/(x+5)) ?
The derivative of x^6(1-1/(x+5)) is (6x^7+55x^6+120x^5)/((x+5)^2)
What is the first derivative of x^6(1-1/(x+5)) ?
The first derivative of x^6(1-1/(x+5)) is (6x^7+55x^6+120x^5)/((x+5)^2)