Question

fie f:D->R ,f(x)= arcsin x/radical din 1plus x la a doua
$\frac{x}{ \sqrt{1 + {x}^{2} } }$
. Sa se calculeze f' (A)
URGENT , VA ROOGG
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Answer 1

Răspuns:

Aplicui formula

(arcsin u) `= u `/√(1-u²)  unde

u(x)=x/√(1+x²)

u `(x)=[x`*√(1+x²)-x*√(1+x²)`]/√(1+x²)²=

(√(1+x²)-x*2x/2√(1+x²)/(1+x²)=

(√(1+x²)-x²/√(1+x²))/(1+x²)=

(√(1+x²)²-x²)/(1+x²)*√(1+x²)=

(1+x²-x²)/(1+x²)√(1+x²)=1/(1+x²)√(1+x²)

---------

√(1-u²x)=√[1-(x/√1+x²)²=

√[1-x²/(1+x²)=√(1+x²-x²)/(1+x²)=

1/√(1+x²)

u `(x)/u(x)=1/(1+x²)*√(1+x²):(1/√(1+x²)=

√(1+x²)/(1+x²)*√(1+x²)=

1/(1+x²)

Explicație pas cu pas: