Warm up (10/24/19)

Front

What is the Power Rule in differentiation?

Back

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

Front

What is the Chain Rule in differentiation?

Back

The Chain Rule is used to differentiate composite functions. If f(g(x)) is a composite function, then its derivative is f'(g(x)) * g'(x).

Front

What is the Quotient Rule in differentiation?

Back

The Quotient Rule is used to differentiate functions that are ratios of two functions. If f(x) = u(x)/v(x), then f'(x) = (u'v - uv')/v^2.

Front

Differentiate the function f(x) = 6x^(2/3).

Back

f'(x) = 4x^(-1/3).

Front

What is the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).

Front

Differentiate the function f(x) = (3x^2 - 2)cos(x^3 - 2x).

Back

Using the product rule, f'(x) = (3x^2 - 2)(-sin(x^3 - 2x)(3x^2 - 2)) + cos(x^3 - 2x)(6x).

Front

What is the difference between the Power Rule and the Chain Rule?

Back

The Power Rule applies to functions of the form x^n, while the Chain Rule applies to composite functions where one function is inside another.

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.

Front

Differentiate the function f(x) = x^5 + 3x^3 - 2x + 7.

Back

f'(x) = 5x^4 + 9x^2 - 2.