Find the derivative of the function.h(x) = ex6 − x + 5

To find the derivative of the function h(x) = e^(x^6) - x + 5, we will use the chain rule and the power rule.

The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. The power rule states that the derivative of x^n is n*x^(n-1).

Step 1: Identify the outer and inner functions for the first term. The outer function is e^u and the inner function is x^6.

Step 2: Take the derivative of the outer function, which is e^u.

Step 3: Take the derivative of the inner function, which is 6x^5 (using the power rule).

Step 4: Multiply the results from steps 2 and 3 to get the derivative of the first term. This gives us 6x^5 * e^(x^6).

Step 5: Take the derivative of the second term, -x, which is -1 (using the power rule with n=1).

Step 6: The derivative of the constant term, 5, is 0.

Step 7: Combine the results from steps 4, 5, and 6 to get the derivative of the entire function: h'(x) = 6x^5 * e^(x^6) - 1 + 0.

So, the derivative of the function h(x) = e^(x^6) - x + 5 is h'(x) = 6x^5 * e^(x^6) - 1.