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

The derivative of 7^{x^7} is ln(7)*7^{x^7+1}x^6

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

The first derivative of 7^{x^7} is ln(7)*7^{x^7+1}x^6

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derivative of

7^{x^{7}}

ln (7) \cdot 7^{x^{7} + 1} x^{6}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{x^{7} l n (7)} \cdot 7 ln (7) x^{6} : ln (7) \cdot 7^{x^{7} + 1} x^{6}

= ln (7) \cdot 7^{x^{7} + 1} x^{6}

What is the derivative of 7^{x^7} ?
The derivative of 7^{x^7} is ln(7)*7^{x^7+1}x^6
What is the first derivative of 7^{x^7} ?
The first derivative of 7^{x^7} is ln(7)*7^{x^7+1}x^6