Mixed Derivatives Practice (Product, Quotient, Chain, Power)

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

What is the Power Rule for derivatives?

Back

If y = x^n, then y' = n*x^(n-1).

Front

What is the Product Rule for derivatives?

Back

If y = u*v, then y' = u'v + uv'.

Front

What is the Quotient Rule for derivatives?

Back

If y = u/v, then y' = (u'v - uv')/v^2.

Front

What is the Chain Rule for derivatives?

Back

If y = f(g(x)), then y' = f'(g(x)) * g'(x).

Front

Find the derivative of y = 3x^4 + 5x^2 - 7.

Back

y' = 12x^3 + 10x.

Front

Find the derivative of y = sin(x) + cos(x).

Back

y' = cos(x) - sin(x).

Front

Find the derivative of y = e^(2x).

Back

y' = 2e^(2x).

Front

Find the derivative of y = ln(x^2 + 1).

Back

y' = (2x)/(x^2 + 1).

Front

Find the derivative of y = (x^2 + 1)/(x - 1).

Back

y' = (2x(x - 1) - (x^2 + 1))/(x - 1)^2.