chain rule
sin(3x)
3cos(3x)
x^2=3y
dy/dx=(2x)/3
tan^-1x
dy/dx=1/(1+x^2)
y=x^4+3x
(d^2y)/dx^2=12x^2
3sin(y+6x)=x^5, fi nd dy/dx
dy/dx=(5x^4-6)/(3cos(y+6x)
3e^(3x)
9e^(3x)
x^3-e^x=e^y-2y
dy/dx=(3x-e^x)/(e^y-2)
sin^-1x
dy/dx=1/(sqrt(1-x^2))
y=x^5+sinx
(d^2y)/dx^2=16x^2-sinx
y=tan^-1(x^2+2), fi nd dy/dx
dy/dx=(2x)/(1+(x^2+2)^2
-6cos(2x^2)
24xsin(2x^2)
x+siny=-cosx
dy/dx=(sinx-1)/cosy
cos^-1x
dy/dx=-1/sqrt(1-x^2)
y=sqrt(x)+x^-2
(d^2y)/dx^2=-1/4x^(-3/2)+6x^-4
y=root(3)x +5x^4 , fi nd (d^2y)/dx^2
(d^2y)/dx^2=-2/9x^(-5/3)+60x^2
(6x+x^2)^2
4x^3+36x^2+72x
6x^3-x^2+3x=y^2+3y
(18x^2-2x+3)/(2y+3)
sec^-1x
dy/dx=1/(|x|sqrt(x^2-1))
y=sinx+ln(5x)
(d^2y)/dx^2=-sinx(-5/x^2)
if y=sin^2x+e^x , then (d^2y)/dx^2 =
(d^2y)/dx^2= -2sin^2x+2cos^2x+e^x
(log_5x+2x^2)^4
4(log_5x+2x^2)(lnx/ln5 +4x)
6xy^2+e^(y+7)=cos^2x
dy/dx=(-2cosxsinx-6y^2)/(12xy+e^(y+7))
csc^-1x
dy/dx=-1/(|x|sqrt(x^2-1))
y=e^x*x+2x^2
(d^2y)/dx^2=xe^x+e^x+4x
4y^2=2(sin(y)-lnx)^(1/3)+sqrty
dy/dx=(2/3(siny-lnx)^(-2/3))/(8y-(1/2)y^(-1/2)