Final answer:
To find the derivative of the given function f(x) = 105 √x³ - √x7 + 63 √x8 − 3, use the power rule of differentiation. Find the derivative of each term and then sum up the derivatives to find the overall derivative of the function.
Step-by-step explanation:
To find the derivative of the given function f(x) = 105 √x³ - √x7 + 63 √x8 − 3, we can use the power rule of differentiation. The power rule states that the derivative of x^n is n*x^(n-1).
In this case, we have three terms in the function: 105 √x³, - √x7, and 63 √x8. Let's find the derivative of each term separately.
For the first term, 105 √x³, the derivative would be (105/2) * x^(3/2 - 1).
For the second term, - √x7, the derivative would be (-1/2) * x^(7/2 - 1).
For the third term, 63 √x8, the derivative would be (63/2) * x^(8/2 - 1).
Finally, sum up these three derivatives to find the derivative of the entire function.