Calculus Derivatives

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

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

Back

dy/dx = 3x^2 + 4x - 5.

Front

What is the product rule for differentiation?

Back

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

Front

What is the quotient rule for differentiation?

Back

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

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 chain rule for differentiation?

Back

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

Front

Find the second derivative of f(x) = x^2 + 3x + 2.

Back

f''(x) = 2.

Front

What is the derivative of y = ln(x)?

Back

dy/dx = 1/x.