Let y = xx + cos(x). Find y′.A. y′ = xxx−1 − sin(x)B. y′ = xx(ln(x) + 1)C. y′ = y(ln(x) + 1)D. y′ = xx(ln(x) + 1) − sin(x)E. y′ = y(ln(x) + 1) + sin(x)

Question

Let y = xx + cos(x). Find y′.

A. y′ = xxx−1 − sin(x)
B. y′ = xx(ln(x) + 1)
C. y′ = y(ln(x) + 1)
D. y′ = xx(ln(x) + 1) − sin(x)
E. y′ = y(ln(x) + 1) + sin(x)

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Solution

The derivative of the function y = xx + cos(x) can be found by using the rules of differentiation.

The derivative of xx is a special case and can be found using the formula for the derivative of a^u, which is a^u * u' * ln(a). Here, a = x and u = x, so the derivative is xx * 1 * ln(x) + xx * x' = xx(ln(x) + 1).

The derivative of cos(x) is -sin(x).

So, the derivative of the function y = xx + cos(x) is xx(ln(x) + 1) - sin(x).

Therefore, the correct answer is D. y′ = xx(ln(x) + 1) − sin(x).

This problem has been solved

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