What is the derivative of (9x^8-8x^9)((x+1)/x) ?

The derivative of (9x^8-8x^9)((x+1)/x) is -72x^8+8x^7+63x^6

What is the first derivative of (9x^8-8x^9)((x+1)/x) ?

The first derivative of (9x^8-8x^9)((x+1)/x) is -72x^8+8x^7+63x^6

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derivative of

(9 x^{8} - 8 x^{9}) (\frac{x + 1}{x})

- 72 x^{8} + 8 x^{7} + 63 x^{6}

Solution steps

\frac{d}{d x} ((9 x^{8} - 8 x^{9}) \frac{x + 1}{x})

Simplify

(9 x^{8} - 8 x^{9}) \frac{x + 1}{x} : x^{7} (x + 1) (- 8 x + 9)

= \frac{d}{d x} (x^{7} (x + 1) (- 8 x + 9))

Apply the Product Rule:

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

f = x^{7}, g = (x + 1) (- 8 x + 9)

= \frac{d}{d x} (x^{7}) (x + 1) (- 8 x + 9) + \frac{d}{d x} ((x + 1) (- 8 x + 9)) x^{7}

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

\frac{d}{d x} ((x + 1) (- 8 x + 9)) = - 16 x + 1

= 7 x^{6} (x + 1) (- 8 x + 9) + (- 16 x + 1) x^{7}

Simplify

7 x^{6} (x + 1) (- 8 x + 9) + (- 16 x + 1) x^{7} : - 72 x^{8} + 8 x^{7} + 63 x^{6}

= - 72 x^{8} + 8 x^{7} + 63 x^{6}

lo g_{10} (2^{x} + 2^{- x})

\frac{d}{d n} (i^{2 n})

cot (x^{4})

(x + 2) (x^{3} - 1)

\frac{d}{dd} (d + 14)

What is the derivative of (9x^8-8x^9)((x+1)/x) ?
The derivative of (9x^8-8x^9)((x+1)/x) is -72x^8+8x^7+63x^6
What is the first derivative of (9x^8-8x^9)((x+1)/x) ?
The first derivative of (9x^8-8x^9)((x+1)/x) is -72x^8+8x^7+63x^6