What´s is the derivate of y=sin(3x^2) ?

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Answer 1 · 2018-05-22T23:45:46

#dy/dx=6xcos(3x^2)#

We're dealing with a composite function here, so it helps to use the Chain Rule

#f'(g(x))*g'(x)#

Our #f(x)# is the outside function, #sinx#, and our inside function, #g(x)# is #3x^2#.

So far, we know

#f(x)=sinx=>color(blue)(f'(x)=cosx)# (Derivatives of trig functions)

#color(red)(g(x)=3x^2)=>color(lime)(g'(x)=6x)# (From the Power Rule)

Now, let's plug into our expression for the Chain Rule. We get

#dy/dx=color(blue)(coscolor(red)((3x^2)))*color(lime)(6x)#

which can be rewritten as

#dy/dx=6xcos(3x^2)#

Hope this helps!