3. Differentiate the following w.r.t. x: 

e ^x^{ ^3}

Answers (1)

Given function is
f(x)=e ^{x^3}
Let g(x)=x^3
Then,
f(x)=e^{g(x)}
Now, differentiation w.r.t. x
f^{'}(x)=g^{'}(x).e^{g(x)}                   -(i)
g(x) = x^3 \Rightarrow g^{'}(x ) =3x^2 
Put this value in our equation (i)
f^{'}(x) =3x^2.e^{x^3}
Therefore, the answer is 3x^2.e^{x^3}

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