Product/Quotient Rule of Derivatives (Delehant)

Front

What is the Product Rule of Derivatives?

Back

The Product Rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: (u*v)' = u'v + uv'.

Front

What is the Quotient Rule of Derivatives?

Back

The Quotient Rule states that if you have a function that is the quotient of two functions u(x) and v(x), the derivative is given by: (u/v)' = (u'v - uv')/v^2.

Front

Find the derivative of g(x)=(3x-2)/(x^2+2).

Back

g'(x) = (-3x^2 + 4x + 6)/(x^2 + 2)^2.

Front

Find f''(1) if f(x)=(x^2-2x-1)/(3x).

Back

f''(1) = -2/3.

Front

Given that y = (x+2)/(x-3), find y'.

Back

y' = -5/(x-3)^2.

Front

Find f'(x) if f(x)=(2x-7)/(x+3).

Back

f'(x) = 13/(x+3)^2.

Front

Find the derivative of y = 2x^2(3x - 4).

Back

y' = 18x^2 - 16x.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

How do you apply the Product Rule in differentiation?

Back

To apply the Product Rule, differentiate each function separately, multiply the derivative of the first function by the second function, and add the product of the first function and the derivative of the second function.

Front

How do you apply the Quotient Rule in differentiation?

Back

To apply the Quotient Rule, differentiate the numerator and denominator separately, multiply the derivative of the numerator by the denominator, subtract the product of the numerator and the derivative of the denominator, and divide by the square of the denominator.