What is the derivative of (ln(3)+e^{x^e})^e ?

The derivative of (ln(3)+e^{x^e})^e is e^{x^e+2}x^{e-1}(ln(3)+e^{x^e})^{e-1}

What is the first derivative of (ln(3)+e^{x^e})^e ?

The first derivative of (ln(3)+e^{x^e})^e is e^{x^e+2}x^{e-1}(ln(3)+e^{x^e})^{e-1}

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derivative of

(ln (3) + e^{x^{e}})^{e}

e^{x^{e} + 2} x^{e - 1} (ln (3) + e^{x^{e}})^{e - 1}

Solution steps

\frac{d}{d x} ((ln (3) + e^{x^{e}})^{e})

Apply the chain rule:

e (ln (3) + e^{x^{e}})^{e - 1} \frac{d}{d x} (ln (3) + e^{x^{e}})

= e (ln (3) + e^{x^{e}})^{e - 1} \frac{d}{d x} (ln (3) + e^{x^{e}})

\frac{d}{d x} (ln (3) + e^{x^{e}}) = e^{x^{e} + 1} x^{e - 1}

= e (ln (3) + e^{x^{e}})^{e - 1} e^{x^{e} + 1} x^{e - 1}

Simplify

e (ln (3) + e^{x^{e}})^{e - 1} e^{x^{e} + 1} x^{e - 1} : e^{x^{e} + 2} x^{e - 1} (ln (3) + e^{x^{e}})^{e - 1}

= e^{x^{e} + 2} x^{e - 1} (ln (3) + e^{x^{e}})^{e - 1}

x \to - 1 + lim (1 - x^{2})

\int \frac{1}{( 1 + x ^{2} ) ( 1 + arctan ( x ) )} d x

x \to 7 lim (e^{x} - e^{- x} - x)

9 x^{2} + 2 x, at x = 3

\int 2^{x} e^{x} d x

What is the derivative of (ln(3)+e^{x^e})^e ?
The derivative of (ln(3)+e^{x^e})^e is e^{x^e+2}x^{e-1}(ln(3)+e^{x^e})^{e-1}
What is the first derivative of (ln(3)+e^{x^e})^e ?
The first derivative of (ln(3)+e^{x^e})^e is e^{x^e+2}x^{e-1}(ln(3)+e^{x^e})^{e-1}