Derivatives - calc

Question

Compute the following derivatives. Assume a and b are constants, f and g are functions, and x is the input variable. Your answers may include any or all of the symbols x, a, b, f and g, as well as the derivatives of f and g.

1.y = x^2f

y' =_____________

2.y = a + bf/g

y' =_____________

3.y = x + f/g

y' =_____________

4.y = (x + f)^3

y' =_____________

5.y = ax^2 + bg^2 + f

y' =_____________

Answer 1

1) y^' = 2xf + x²f^' (by product rule)

2) y^' = (bf^'g - bfg^') / g² (by quotient rule).

3) y^' = 1 + (f^'g - g^'f) / g² (see 2)

4) y^' = 3(1 + f^')(x + f)² (by chain rule)

5) y^' = 2ax + 2bgg^' + f^'.