For , the difference quotient is . After factorising from the numerator, which…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For f(x)=x5f(x)=x^{5}, the difference quotient is f(x+h)−f(x)h\displaystyle \frac{f(x+h)-f(x)}{h}. After factorising hh from the numerator, which expression remains in the numerator? (a) 5x4+5x3h+5x2h2+5xh3+h45x^{4}+5x^{3}h+5x^{2}h^{2}+5xh^{3}+h^{4} (b) 5x4+10x3h+10x2h2+h55x^{4}+10x^{3}h+10x^{2}h^{2}+h^{5} (c) 5x4+10x3h+10x2h2+5xh3+h45x^{4}+10x^{3}h+10x^{2}h^{2}+5xh^{3}+h^{4} (d) 5x4+10x3h+10x2h2+5xh35x^{4}+10x^{3}h+10x^{2}h^{2}+5xh^{3}

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