Finding Derivatives of Functions

Front

What is the derivative of a function?

Back

The derivative of a function measures how the function's output value changes as its input value changes. It represents the slope of the tangent line to the function's graph at a given point.

Front

What is the power rule for differentiation?

Back

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

Front

How do you differentiate a quotient of two functions?

Back

To differentiate a quotient of two functions, use the quotient rule: if f(x) = g(x)/h(x), then f'(x) = (g'(x)h(x) - g(x)h'(x)) / (h(x))^2.

Front

What is the product rule for differentiation?

Back

The product rule states that if f(x) = g(x) * h(x), then f'(x) = g'(x)h(x) + g(x)h'(x).

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

What is the derivative of tan(x)?

Back

The derivative of tan(x) is sec^2(x).

Front

How do you differentiate a logarithmic function?

Back

To differentiate a logarithmic function, use the rule: if f(x) = ln(g(x)), then f'(x) = g'(x)/g(x).

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y = f(g(x)), then the derivative is f'(g(x)) * g'(x).

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.