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Popular >

derivative of e^{e^{3x^2}}

Solution

\frac{d}{d x} (e^{e^{3 x^{2}}})

Solution

6 e^{e^{3 x^{2}} + 3 x^{2}} x

Solution steps

\frac{d}{d x} (e^{e^{3 x^{2}}})

Apply the chain rule:

e^{e^{3 x^{2}}} \frac{d}{d x} (e^{3 x^{2}})

= e^{e^{3 x^{2}}} \frac{d}{d x} (e^{3 x^{2}})

\frac{d}{d x} (e^{3 x^{2}}) = e^{3 x^{2}} \cdot 6 x

= e^{e^{3 x^{2}}} e^{3 x^{2}} \cdot 6 x

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{e^{3 x^{2}}} e^{3 x^{2}} = e^{e^{3 x^{2}} + 3 x^{2}}

= 6 e^{e^{3 x^{2}} + 3 x^{2}} x

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Frequently Asked Questions (FAQ)

What is the derivative of e^{e^{3x^2}} ?
The derivative of e^{e^{3x^2}} is 6e^{e^{3x^2}+3x^2}x
What is the first derivative of e^{e^{3x^2}} ?
The first derivative of e^{e^{3x^2}} is 6e^{e^{3x^2}+3x^2}x