# How do you differentiate #y=e^(2x^3)#?

We use Chain Rule here.

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To differentiate ( y = e^{2x^3} ), you would use the chain rule. The chain rule states that if you have a function within another function, you differentiate the outer function first, then multiply it by the derivative of the inner function.

So, for ( y = e^{2x^3} ), the outer function is ( e^u ) where ( u = 2x^3 ).

The derivative of ( e^u ) with respect to ( u ) is ( e^u ).

The derivative of ( u = 2x^3 ) with respect to ( x ) is ( 6x^2 ).

Therefore, using the chain rule, the derivative of ( y = e^{2x^3} ) with respect to ( x ) is ( \frac{dy}{dx} = e^{2x^3} \times 6x^2 = 6x^2e^{2x^3} ).

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