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

Solution

derivative of

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

210 x^{13} - 1274 x^{12} + 3276 x^{11} - 4620 x^{10} + 3850 x^{9} - 1890 x^{8} + 504 x^{7} - 56 x^{6}

Solution steps

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

Simplify

8 x^{7} (x - 1)^{7} + 7 (x - 1)^{6} x^{8} : 15 x^{14} - 98 x^{13} + 273 x^{12} - 420 x^{11} + 385 x^{10} - 210 x^{9} + 63 x^{8} - 8 x^{7}

= \frac{d}{d x} (15 x^{14} - 98 x^{13} + 273 x^{12} - 420 x^{11} + 385 x^{10} - 210 x^{9} + 63 x^{8} - 8 x^{7})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (15 x^{14}) - \frac{d}{d x} (98 x^{13}) + \frac{d}{d x} (273 x^{12}) - \frac{d}{d x} (420 x^{11}) + \frac{d}{d x} (385 x^{10}) - \frac{d}{d x} (210 x^{9}) + \frac{d}{d x} (63 x^{8}) - \frac{d}{d x} (8 x^{7})

\frac{d}{d x} (15 x^{14}) = 210 x^{13}

\frac{d}{d x} (98 x^{13}) = 1274 x^{12}

\frac{d}{d x} (273 x^{12}) = 3276 x^{11}

\frac{d}{d x} (420 x^{11}) = 4620 x^{10}

\frac{d}{d x} (385 x^{10}) = 3850 x^{9}

\frac{d}{d x} (210 x^{9}) = 1890 x^{8}

\frac{d}{d x} (63 x^{8}) = 504 x^{7}

\frac{d}{d x} (8 x^{7}) = 56 x^{6}

= 210 x^{13} - 1274 x^{12} + 3276 x^{11} - 4620 x^{10} + 3850 x^{9} - 1890 x^{8} + 504 x^{7} - 56 x^{6}