What is the derivative of x^8(x-1^7) ?

The derivative of x^8(x-1^7) is 8x^7(x-1)^7+7(x-1)^6x^8

What is the first derivative of x^8(x-1^7) ?

The first derivative of x^8(x-1^7) is 8x^7(x-1)^7+7(x-1)^6x^8

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} ((x - 1)^{7}) = 7 (x - 1)^{6}

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

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