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 you have a function y = f(g(x)), then the derivative dy/dx = f'(g(x)) * g'(x).

Front

Differentiate y = (x^2 + 1)^3 using the Chain Rule.

Back

dy/dx = 3(x^2 + 1)^2 * (2x).

Front

What is the derivative of f(x) = (x^3 - 2x)^2?

Back

f'(x) = 6x^5 - 16x^3 + 8x.

Front

Differentiate f(x) = 7(3x + 4)^5 using the Chain Rule.

Back

f'(x) = 105(3x + 4)^4.

Front

How do you find G'(2) if G(x) is a function?

Back

To find G'(2), you need to evaluate the derivative of G at x = 2.

Front

What does it mean to find the derivative at a specific point, like x=2?

Back

Finding the derivative at a specific point gives the slope of the tangent line to the function at that point.

Front

If f(x) = x^2, what is f'(x) using the power rule?

Back

f'(x) = 2x.

Front

What is the power rule for derivatives?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

Front

Differentiate y = 5x^4 using the power rule.

Back

dy/dx = 20x^3.

Front

What is the product rule in calculus?

Back

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