What is the derivative of 5^{6^{7^x}} ?

The derivative of 5^{6^{7^x}} is ln(5)ln(6)ln(7)*7^x*5^{6^{7^x}}*6^{7^x}

What is the first derivative of 5^{6^{7^x}} ?

The first derivative of 5^{6^{7^x}} is ln(5)ln(6)ln(7)*7^x*5^{6^{7^x}}*6^{7^x}

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\frac{d}{d x} (5^{6^{7^{x}}})

ln (5) ln (6) ln (7) \cdot 7^{x} \cdot 5^{6^{7^{x}}} \cdot 6^{7^{x}}

Solution steps

\frac{d}{d x} (5^{6^{7^{x}}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{6^{7^{x}}} = e^{6^{7^{x}} l n (5)}

= \frac{d}{d x} (e^{6^{7^{x}} l n (5)})

Apply the chain rule:

e^{6^{7^{x}} l n (5)} \frac{d}{d x} (6^{7^{x}} ln (5))

= e^{6^{7^{x}} l n (5)} \frac{d}{d x} (6^{7^{x}} ln (5))

\frac{d}{d x} (6^{7^{x}} ln (5)) = ln (5) ln (6) ln (7) \cdot 7^{x} \cdot 6^{7^{x}}

= e^{6^{7^{x}} l n (5)} ln (5) ln (6) ln (7) \cdot 7^{x} \cdot 6^{7^{x}}

e^{6^{7^{x}} l n (5)} = 5^{6^{7^{x}}}

= ln (5) ln (6) ln (7) \cdot 7^{x} \cdot 5^{6^{7^{x}}} \cdot 6^{7^{x}}

e^{x} y \cdot y^{^{'}} = e^{- y} + e^{- 2 x - y}

f (x) = sin (2 x), - \frac{π}{2}, \frac{π}{6}

\frac{d ^{2}}{d x ^{2}} (11 e^{x^{2}})

(- 1 x - 2)^{10}

- 204 x

What is the derivative of 5^{6^{7^x}} ?
The derivative of 5^{6^{7^x}} is ln(5)ln(6)ln(7)*7^x*5^{6^{7^x}}*6^{7^x}
What is the first derivative of 5^{6^{7^x}} ?
The first derivative of 5^{6^{7^x}} is ln(5)ln(6)ln(7)*7^x*5^{6^{7^x}}*6^{7^x}