Question

Find the derivative of f(x)=(x−9)sqrt(10x⁵+1)

Answer 1

To find the derivative of f(x) = (x-9)√(10x⁵+1), we can use the product rule and the chain rule. The derivative of f(x) is 1/(2√(10x⁵+1)) * (x-9) + √(10x⁵+1).

Step-by-step explanation:

To find the derivative of f(x) = (x-9)√(10x⁵+1), we can use the product rule and the chain rule. Let's differentiate step by step:

1. Take the derivative of (x-9): 1
2. Multiply it with the square root of (10x⁵+1)
3. Take the derivative of the square root of (10x⁵+1): 1/(2√(10x⁵+1))
4. Finally, combine all the parts to get the derivative of f(x)

The derivative of f(x) = (x-9)√(10x⁵+1) is 1/(2√(10x⁵+1)) * (x-9) + √(10x⁵+1).