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Answer :
The derivative of the function f(x) = x^7 is f'(x) = 7x^7.
The given function is f(x) = x7.
Use logarithmic differentiation to determine the derivative.
The logarithmic differentiation of the given function is given by:
ln y = ln (x^7)y = x^7ln y = 7 ln (x)y / x = 7x^6
Differentiating the above expression with respect to x, we get:
y′ / x - y / x² = 42x⁵y′ / x = 7x^6y′ = 7x^7
Hence, the derivative of the function f(x) = x^7 is f'(x) = 7x^7.
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