Y = 2x^3sinx - 3xcosx Find the derivative of the equation?
1 Answer
Mar 4, 2017
Explanation:
Each term has to be differentiated using the
color(blue)"product rule"product rule
"Given "f(x)=g(x).h(x)" then"Given f(x)=g(x).h(x) then
color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))larr" product rule"
color(magenta)"First term"
"for "f(x)= 2x^3sinx
"here "g(x)=2x^3rArrg'(x)=6x^2
h(x)=sinxrArrh'(x)=cosx
rArrf'(x)=2x^3(cosx)+6x^2(sinx)to(1)
color(magenta)"Second term"
f(x)=3xcosx
"here "g(x)=3xrArrg'(x)=3
h(x)=cosxrArrh'(x)=-sinx
rArrf'(x)=3x(-sinx)+3cosxto(2)
"Combining differentiated terms, that is " (1)-(2)
dy/dx=2x^3cosx+6x^2sinx+3xsinx-3cosx
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