chain rule derivatives practice

Front

What is the Chain Rule in calculus?

Back

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. It states that if y = f(g(x)), then the derivative dy/dx = f'(g(x)) * g'(x).

Front

Find the derivative of y = (x^2 + 1)^3 at x = 2.

Back

dy/dx = 3(x^2 + 1)^2(2x) = 3(5)^2(4) = 300.

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

How do you find the slope of the tangent line at a point on a curve?

Back

To find the slope of the tangent line at a point, calculate the derivative of the function at that point.

Front

Find the derivative of y = 5x^5 + 5.

Back

dy/dx = 25x^4.

Front

What is the derivative of y = x^n?

Back

The derivative is dy/dx = n*x^(n-1).

Front

Find the derivative of y = sin(x).

Back

dy/dx = cos(x).

Front

Find the derivative of y = e^x.

Back

dy/dx = e^x.

Front

What is the product rule?

Back

The product rule states that if u and v are functions of x, then the derivative of their product is (uv)' = u'v + uv'.

Front

What is the quotient rule?

Back

The quotient rule states that if u and v are functions of x, then the derivative of their quotient is (u/v)' = (u'v - uv')/v^2.