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Popular >

derivative of 7^{x^7}

Solution

derivative of

7^{x^{7}}

Solution

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}

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\int \frac{x}{( a ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x

(\partial)/(\partial y)(x^{yz})

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(\partial)/(\partial x)(ln(9x^2+4y^2+5))

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Frequently Asked Questions (FAQ)

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