Question

Find the derivative with respect to x of y = (3x + x2)5. A. (3 + 2x) 5 B. 5(3x + x2)4(3 + 2x) C. 5(3x + x2)4 D. 5(3 + 2x)4

Answer 1

y = 3x +x²


`(dy)/(dx) = d((3x+ x^(2)) )/(dx) = 3 (dx)/(dx) +d ( (x^(2)) )/(dx)`
=
`3 + 2x (dx)/(dx) = 3+2x`

Answer 2

When you have a function that is in the form of (f(x))^n, the derivative of the function will have the formula:
n * (f(x))^(n-1) * f'(x)

The given function is:
y = (3x+x^2) ^ 5

Based on the above, the derivative with respect to x would be:
5 * (3x+x^2)^(5-1) * f'(3x+x^2)
This would give a result of:
5 * (3x+x^2)^4 * (3+2x)

Comparing the calculated derivative with the given choices, the right choice would be:
B. 5 * (3x+x^2)^4 * (3+2x)