Question

Differentiate the following functions: (ax)^m + b^m

A) (ma * (ax)^(m-1))
B) (ma * (ax)^m)
C) (ma * (ax)^(m+1))
D) (m * (ax)^(m-1))

Answer 1

To differentiate the function (ax)^m + b^m, we can use the power rule of differentiation. The derivative of (ax)^m is am(m)(ax)^(m-1), and the derivative of b^m is 0.

Step-by-step explanation:

To differentiate the function (ax)^m + b^m, we can use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = cx^n, where c and n are constants, then the derivative of f(x) is given by f'(x) = ncx^(n-1). Applying this rule to our given function, we can differentiate each term separately.

The first term (ax)^m can be written as amx^m. Taking the derivative, we get (am)(mx)^(m-1) = am(m)(ax)^(m-1). For the second term b^m, since b is a constant, its derivative is 0.

Therefore, the derivative of (ax)^m + b^m is am(m)(ax)^(m-1).

Answer 2

To differentiate the function (ax)^m + b^m, we apply the power rule to the term (ax)^m, resulting in ma(ax)^(m-1), and the constant term b^m differentiates to zero. The correct answer is D) (m * (ax)^(m-1)).

Step-by-step explanation:

The student is asking how to differentiate the function (ax)m + bm. To differentiate this function, we will use the power rule of differentiation, which states that if f(x) = xn, then f'(x) = nxn-1. The constant term bm, where b is a constant and m is an exponent, is not dependent on x and its derivative will be zero.

Therefore, when we differentiate (ax)m, we get ma(ax)m-1. The second term, bm, being a constant in terms of x, its derivative is zero. Putting these together, the derivative of the original function is ma(ax)m-1.

So, the correct answer is D) (m * (ax)m-1).