## [數學][問題]求導數

### [數學][問題]求導數

f(x)=ex/(1+ex)
f'(x)=(ex(1+ex)-exex)/(1+ex)2
=1/(1+ex)2

f(x)=(3-x)/(x ln x)
f'(x)=(-(x ln x)-(3-x)(x(1/x)+ln x))/(x ln x)2
=(-x ln x -(3-x+3ln x -x ln x))/(x ln x)2
=(-3+x-3ln x)/(x ln x)2

f(x)=ln ((x2-4)/(ex+1))
f'(x)=((2x(ex+1)-(x2-4)ex)/(ex+1)2)/((x2-4)/(ex+1))
=((2x(ex+1)-(x2-4)ex)/(x2-4)(ex+1)
=2x/(x2-4)-ex/(ex+1)

ET外星人

ET外星人 寫到:
f(x)=e<SUP>x</SUP>/(1+e<SUP>x</SUP>)
f'(x)=(e<SUP>x</SUP>(1+e<SUP>x</SUP>)-e<SUP>x</SUP>e<SUP>x</SUP>)/(1+e<SUP>x</SUP>)<SUP>2</SUP>
<SUP>       </SUP>=1/(1+e<SUP>x</SUP>)<SUP>2</SUP>

f(x)=(3-x)/(x ln x)
f'(x)=(-(x ln x)-(3-x)(x(1/x)+ln x))/(x ln x)<SUP>2</SUP>
=(-x ln x -(3-x+3ln x -x ln x))/(x ln x)<SUP>2</SUP>
=(-3+x-3ln x)/(x ln x)<SUP>2</SUP>

f(x)=ln ((x<SUP>2</SUP>-4)/(e<SUP>x</SUP>+1))
f'(x)=((2x(e<SUP>x</SUP>+1)-(x<SUP>2</SUP>-4)e<SUP>x</SUP>)/(e<SUP>x</SUP>+1)<SUP>2</SUP>)/((x<SUP>2</SUP>-4)/(e<SUP>x</SUP>+1))
=((2x(e<SUP>x</SUP>+1)-(x<SUP>2</SUP>-4)e<SUP>x</SUP>)/(x<SUP>2</SUP>-4)(e<SUP>x</SUP>+1)
=2x/(x<SUP>2</SUP>-4)-e<SUP>x</SUP>/(e<SUP>x</SUP>+1)

f'(x)= e^x/(e^x+1) ^2

f(x)=ln(x^2-4)-ln(e^x+1)
f'(x)=2x/(x^2-4)- e^x/(e^x+1)