Find the derivative of the given function. Use all lower case letters.h(x) = ax3 + bch'(x) =

The derivative of the function h(x) = ax^3 + b can be found using the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).

Step 1: Identify the terms in the function. Here, we have two terms: ax^3 and b.

Step 2: Apply the power rule to each term.

For the first term, ax^3, the power rule gives us 3*ax^(3-1) = 3ax^2.

The second term, b, is a constant. The derivative of a constant is zero.

Step 3: Combine the derivatives of the individual terms to get the derivative of the whole function.

So, the derivative of the function h(x) = ax^3 + b is h'(x) = 3ax^2 + 0 = 3ax^2.