What is the derivative and second derivative of #cos(-x)#?

1 Answer
Jul 2, 2015

#d/dxcos(-x)=\color(blue)(sin(-x))# and #d/(d^2x)cos(-x)=\color(green)(-cos(-x))#

Explanation:

#d/dxcos(-x)=d/dx(-x)d/(d(-x))cos(-x)#
..... used the chain rule
#d/dxcos(-x)=-1*-sin(-x)=\color(blue)(sin(-x)#
..... derivative of #cos(x)=-sin(x)#

#d/(d^2x)cos(-x)=d/dx(d/dxcos(-x))=d/dx(\color(blue)(sin(-x)))#
..... second derivative is derivative of first derivative
#d/(d^2x)cos(-x) = d/dx(-x)d/(d(-x))sin(-x)#
..... used the chain rule again
#d/(d^2x)cos(-x)=-1*cos(-x) = \color(green)(-cos(-x)#
..... derivative of #sin(x)=cos(x)#