Question

find the derivative f(x)=(x³-2x)⁴(x²+7)-2


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Answer 1

Answer:

d/dx((x³+2)(x²+2)/(x³+1)) = d/dx((x⁵+2x³+2x²+4)/(x³+1))

=((x³+1)(x⁵+2x³+2x²+4)′-(x⁵+2x³+2x²+4)(x³+1)′)/(x³+1)²

=((x³+1)(5x⁴+6x²+4x)-(x⁵+2x³+2x²+4)(3x²))/(x³+1)²

=(5x⁷+6x⁵+4x⁴+5x⁴+6x²+4x-3x⁷-6x⁵-6x⁴-12x²)/(x³+1)²

=(2x⁷+3x⁴-6x²+4x)/(x³+1)²

Now, factor the top, just to be sure nothing cancels out:

=x(2x⁶+3x³-6x+4)/(x³+1)². Nothing can cancel, so you can leave it as you had it before:

=(2x⁷+3x⁴-6x²+4x)/(x³+1)²