What is the derivative of e^{e^{e^{e^x}}} ?

The derivative of e^{e^{e^{e^x}}} is e^{e^{e^{e^x}}+e^{e^x}+e^x+x}

What is the first derivative of e^{e^{e^{e^x}}} ?

The first derivative of e^{e^{e^{e^x}}} is e^{e^{e^{e^x}}+e^{e^x}+e^x+x}

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

e^{e^{e^{e^{x}}} + e^{e^{x}} + e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (e^{e^{e^{x}}}) = e^{e^{e^{x}} + e^{x} + x}

= e^{e^{e^{e^{x}}}} e^{e^{e^{x}} + e^{x} + x}

Apply exponent rule:

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

e^{e^{e^{e^{x}}}} e^{e^{e^{x}} + e^{x} + x} = e^{e^{e^{e^{x}}} + e^{e^{x}} + e^{x} + x}

= e^{e^{e^{e^{x}}} + e^{e^{x}} + e^{x} + x}

\int r^{2} d r

x \to 0 lim (\frac{7 x}{cot ( x )})

\frac{\partial}{\partial s} (s sin (t))

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

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