Calc Derivative Rules

Question 0

Power Rule

Answer 0

If x is a positive integer, then y’(x^n) = nxˆn-1
y’(4x²)=8x
y’(3x⁴)=12x³

Question 1

Derivative of a Constant

Answer 1

Derivative of a constant is 0
f(-2)=0
f(110)=0

Question 2

Constant Multiple Rule

Answer 2

The derivative of a number times a function is the number times derivative of the function
y’(cf(x))=cy’(f(x))
(cf’)=c(f’)
y’(6x³)=6y’(x³)=6(3x²)=18x²

Question 3

Sum and Difference Rule

Answer 3

If f and g are differentiable functions, then y’(f(x)+g(x))=y’(f(x))+y’(g(x))
y = x³ - 5x² - 3x - 2 = 3x² -10x -3

Question 4

Product Rule

Answer 4

If f and g are differentiable function of x, then f’(f(x)g(x)) =
(f x g’)+(g x f’)

Question 5

Quotient Rule

Answer 5

If f and g are differentiable functions of x and g(x)≠0:

f(x))/(g(x)) = ((g x f’)-(f x g’))/(g²