Question

After Using The Chain Rule, The Derivative Of A Function Is F′(X)=9(X5+X3)8(5x4+3x2).

A True
B False

Answer 1

The given function's derivative f'(x) = 9(x^5+x^3)^8(5x^4+3x^2) is correctly computed using the Chain Rule. The process involves differentiating the inner function and multiplying it by the derivative of the outer function raised to the power minus one.

Step-by-step explanation:

A student has asked whether the derivative of a function is f'(x) = 9(x5+x3)8(5x4+3x2) after using the Chain Rule. To verify this, we need to apply the Chain Rule correctly to the original function. The Chain Rule in calculus is a formula to compute the derivative of a composite function. If we have a composite function h(x) = g(f(x)), then its derivative h'(x) is given by g'(f(x))·f'(x).

Let's assume the original function is (x5+x3)9. By applying the Chain Rule:

1. Identify the outer function g(u) = u9 and the inner function f(x) = x5 + x3.
2. Compute the derivative of the outer function with respect to its argument u: g'(u) = 9u8.
3. Compute the derivative of the inner function with respect to x: f'(x) = 5x4 + 3x2.
4. Apply the Chain Rule to get h'(x) = g'(f(x))·f'(x) = 9(x5+x3)8(5x4+3x2), which matches the given derivative.

Therefore, the statement is True.