For , which of the following is…

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

Problem

For g(x)=e5xx2+1g(x)=\dfrac{e^{5x}}{x^{2}+1}, which of the following is g′(x)g'(x)? (a) 5e5x(x2+1)2−2xe5xx2+1\displaystyle \frac{5e^{5x}}{(x^{2}+1)^{2}}-\frac{2xe^{5x}}{x^{2}+1} (b) 5e5xx2+1+2xe5x(x2+1)2\displaystyle \frac{5e^{5x}}{x^{2}+1}+\frac{2xe^{5x}}{(x^{2}+1)^{2}} (c) e5x[5(x2+1)−2x](x2+1)2\displaystyle \frac{e^{5x}\bigl[5(x^{2}+1)-2x\bigr]}{(x^{2}+1)^{2}} (d) e5x[(x2+1)−2x](x2+1)2\displaystyle \frac{e^{5x}\bigl[(x^{2}+1)-2x\bigr]}{(x^{2}+1)^{2}}

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