What is the derivative?

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1 Answer
Feb 6, 2018

#(d^3y)/(dx^3)=81sin(3x)#

Explanation:

#"differentiate 3 times using the "color(blue)"chain rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#y=3cos(3x)#

#rArrdy/dx=-3sin(3x)xxd/dx(3x)=-9sin(3x)#

#rArr(d^2y)/(dx^2)=-9cos(3x)xxd/dx(3x)=-27cos(3x)#

#rArr(d^3y)/(dx^3)=27sin(3x)xxd/dx(3x)=81sin(3x)#