How do you differentiate f(x) = sin(x²)?

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Answer 1 · 2018-07-22T12:50:52

#(df)/(dx)=2xcos(x^2)#

Let #f(x)=sin(g(x))# and #g(x)=x^2#

hence #(df)/(dx)=(df)/(dg)xx(dg)/(dx)#

= #cos(g(x))xx2x#

= #2xcos(g(x))#

= #2xcos(x^2)#

Answer 2 · 2018-07-22T13:06:50

#f'(x)=2x\cos(x^2)#

Given function:

#f(x)=\sin(x^2)#

Differentiating above function w.r.t. #x# using chain rule:

#d/dxf(x)=d/dx\sin(x^2)#

#f'(x)=\cos(x^2)\frac{d}{dx}(x^2)#

#=\cos(x^2)(2x)#

#=2x\cos(x^2)#