Basic Derivative Rules (Including Trig)

Front

What is a derivative?

Back

A derivative represents the rate at which a function is changing at any given point, specifically the slope of the tangent line to the curve of the function.

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

The power rule states that if y = x^n, then dy/dx = n*x^(n-1), where n is a constant.

Front

What is the derivative of y = x^4?

Back

dy/dx = 4x^3.

Front

What is the product rule for derivatives?

Back

The product rule states that if u and v are functions of x, then d(uv)/dx = u'v + uv'.

Front

Find dy/dx if y = 3x^2 + 5x - 7.

Back

dy/dx = 6x + 5.

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 chain rule for derivatives?

Back

The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

Find dy/dx if y = e^x.

Back

dy/dx = e^x.