(c)'=0

(xⁿ)'=nx^n-1

(sinx)'=cos

(cosx)'=-sinx

(tgx)'=
=1+tg²x

(ctgx)'=
=1-ctg²x

(a^x)'=a^xlna a<>0

(e^x)'=e^x

(
)'=

(arcsinx)'=

(arccosx)'=

(arctgx)'=

(arcctg)'=

(log_ax)'=

(lnx)'=

(cf(x))'=cf'(x)

(f(x)+g(x))'= f'(x)+g'(x)

(f(x)-g(x))'=f'(x)-g'(x)

(f(x)*g(x))'=f'(x)*g(x)+f(x)*g'(x)

g(x)<>0
=(f'(x)*g(x)-f(x)*g'(x))/(g²(x))

=((e^x)'*lnx-e^x(lnx)”)/(ln²x)=(e^xlnx-e^x*1/x)/(ln²x)

(f(x)^g(x)')=((e^lnf(x))^g(x))=(e^g(xlnf(x))'=e^g(x)lnf(x)*g^(x)lnf(x)= f(x)^g(x)(g'(x)lnf(x)+g(x)/f(x)*f'(x))

f(g(x))'=f'(g(x)*g'(x))

(e^x)⁽ⁿ⁾=e^x

sinx⁽ⁿ⁾=sin(x+(n*pi)/2)

cosx⁽ⁿ⁾=

(tg²x)=2tg*1/(cos²x)

(1+x⁴)³=3(1+x⁴)*4x³

((2²)^x)'=((2²)^x)*ln2*(2^x)'=2²*ln2*2^x*ln2

(2^lnx)'=2^lnx*ln2*1/x

(sin(lnx))“=(cos(lnx))'*1/x+coslnx*(1/x)'= -sinlnx*1/x+coslnx*(-1x^-2)

=((lnx)^1/3)'=1/3*lnx^-2/3*1/x

(x^x)'=e^xlnx*(xlnx)'=x^x(lnx+1)

=
*(
ln
*0,5
)=

(x^sinx)'=(sinxlnx+sinx/x*x')= x^sinx(cosxlnx+sinx/x*1)= x^sinx(coslnx+sinx/x)

(cos(xlnx))'=sin(xlnx)*(xlnx)'=sin(xlnx)*(1*lnx+x*1/x)= sin(xlnx)*(lnx+1)

=(
lnx+
)*

(1/x)'=-1/x²

(lne^x)'=x

(e^lnx)'=x

(arcsin(sinx))'=x

(arctg(tgx))'=x

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