We can use the power rule to find the derivative of f(x) = x^n + x^(n-1). The power rule states that the derivative of x^n is nx^(n-1).
So, the derivative of x^n is nx^(n-1)
And the derivative of x^(n-1) is (n-1)x^(n-2)
So the derivative of f(x) = x^n + x^(n-1) is:
f'(x) = nx^(n-1) + (n-1)x^(n-2)
Now, if we combine the exponents we have :
f'(x) = nx^n-1 + nx^n-2
And we can factor out x^n-2 from the second term, we have:
f'(x) = nx^n-1 + (n-1)x^n-2*x^2
Now, we can simplify the expression by canceling the x^n-2 factor.
f'(x) = nx^n-1 + (n-1)x
And finally, by simplifying the exponent and factoring the constants, we have:
f'(x) = (nx + n - 1) / x^(2-n)
So the derivative of f(x) = x^n + x^(n-1) is f'(x) = (nx + n - 1) / x^(2-n)