Input expression:

x^3+x^2+x+1

Output expression:

3*x^2+2*x+1



Input expression:

sin(cos(x))

Output expression:

-sin(x)*cos(cos(x))



Input expression:

(x^3+2)/x

Output expression:

(3*x^3-(x^3+2))/x^2



Input expression:

x^0.5*(x-1)

Output expression:

x^0.5+0.5*(x-1)/x^0.5



Input expression:

(x-4)^2

Output expression:

2*(x-4)



Input expression:

(7*x+1)*(7*x-1)*(x-1)

Output expression:

(7*x+1)*(7*x-1)+(x-1)*(7*(7*x+1)+7*(7*x-1))



Input expression:

1+1/x+1/x^2+1/x^3

Output expression:

-(1/x^2+2/x^3+3/x^4)



Input expression:

a*x^3+b*x^2+c*x+d

Output expression:

3*a*x^2+2*b*x+c



Input expression:

1/sin(x)

Output expression:

-cos(x)/sin(x)^2



Input expression:

cos(x^2+1)^2

Output expression:

-4*x*sin(x^2+1)*cos(x^2+1)



Input expression:

2*cos(x^2+1)^2

Output expression:

-8*x*sin(x^2+1)*cos(x^2+1)



Input expression:

(exp(x)-exp(-x))^(-1)

Output expression:

-(exp(x)+exp(-x))/(exp(x)-exp(-x))^2



Input expression:

ln(sin(x)/(1-cos(x)))

Output expression:

((1-cos(x))*cos(x)-sin(x)^2)/(sin(x)*(1-cos(x)))



Input expression:

exp(exp(x))

Output expression:

exp(x)*exp(exp(x))



Input expression:

ln(sin(x)*cos(x))

Output expression:

(-sin(x)^2+cos(x)^2)/(sin(x)*cos(x))



Input expression:

1/(x^2+x+1)

Output expression:

-(2*x+1)/(x^2+x+1)^2



Input expression:

ln(sec(x))

Output expression:

tan(x)



Input expression:

cos(x)*sin(x)^3

Output expression:

3*cos(x)^2*sin(x)^2-sin(x)^4



Input expression:

x^sin(x)

Output expression:

(cos(x)*ln(x)+sin(x)/x)*x^sin(x)



Input expression:

(2+ln((1+x)^2))/(2-ln((1-x)^2))

Output expression:

(2*(2-ln((1-x)^2))/(1+x)-2*(2+ln((1+x)^2))/(1-x))/(2-ln((1-x)^2))^2



Input expression:

cosec(x^2)

Output expression:

-2*x*cosec(x^2)*cot(x^2)



Input expression:

cot(x^3)

Output expression:

-3*x^2*cosec(x^3)^2



Input expression:

cosh(x^4+x^3)

Output expression:

(4*x^3+3*x^2)*sinh(x^4+x^3)



Input expression:

sinh(x^3-2*x)

Output expression:

(3*x^2-2)*cosh(x^3-2*x)



Input expression:

tanh(1/x)

Output expression:

-1/x^2*sech(1/x)^2



Input expression:

sech(1+x)

Output expression:

-sech(1+x)*tanh(1+x)



Input expression:

cosech(x^2-x)

Output expression:

-cosech(x^2-x)*(2*x-1)*coth(x^2-x)



Input expression:

coth(x^5+1/x)

Output expression:

-(5*x^4-1/x^2)*cosech(x^5+1/x)^2



Input expression:

ln(cos(x))*ln(sin(x))

Output expression:

ln(cos(x))*cos(x)/sin(x)-ln(sin(x))*sin(x)/cos(x)



Input expression:

sinh(x)^cosh(x)

Output expression:

(sinh(x)*ln(sinh(x))+cosh(x)^2/sinh(x))*sinh(x)^cosh(x)



Input expression:

(sin(x)+cos(x))^(sinh(x)+cosh(x))

Output expression:

((cosh(x)+sinh(x))*ln(sin(x)+cos(x))+(cos(x)-sin(x))*(sinh(x)+cosh(x))/(sin(x)+cos(x)))*(sin(x)+cos(x))^(sinh(x)+cosh(x))



Input expression:

arcsin(x)

Output expression:

1/(1-x^2)^0.5



Input expression:

arcsin((1-x^2)^0.5)

Output expression:

-1/(1-x^2)^0.5



Input expression:

arccos(x)

Output expression:

-1/(1-x^2)^0.5



Input expression:

arctan(x)

Output expression:

1/(1+x^2)



Input expression:

arcsinh(x)

Output expression:

1/(1+x^2)^0.5



Input expression:

arccosh(x)

Output expression:

1/(x^2-1)^0.5



Input expression:

arctanh(x)

Output expression:

1/(1-x^2)



Input expression:

sin(-x^3-3*x^2+2*x-3)

Output expression:

(-(3*x^2+6*x)+2)*cos(-(x^3+3*x^2)+2*x-3)



Input expression:

arctanh(exp(-x^3)*((-x^2-x)-1))

Output expression:

(-exp(-x^3)*(2*x+1)+3*(x^2+x+1)*x^2*exp(-x^3))/(1-(exp(-x^3)*(x^2+x+1))^2)



Input expression:

sin(a*x+b)+cos(c*x+d)

Output expression:

a*cos(a*x+b)-c*sin(c*x+d)