AP Calculus Midterm Review

Front

Find the derivative of the function: x^4 cos(x) - 4x^3 sin(x)

Back

The derivative is: x^4 cos(x) + 4x^3 sin(x)

Front

What is the derivative of cot(x)?

Back

The derivative is: -csc^2(x)

Front

What is the derivative of csc(x)?

Back

The derivative is: -csc(x)cot(x)

Front

When we 'take the derivative' of a function, what are we finding?

Back

We are finding the slope of the tangent line.

Front

Find dy/dx by Implicit Differentiation for the equation: x^3 + y^3 = 36

Back

The derivative dy/dx is: -x^2/y^2.

Front

Define the derivative in calculus.

Back

The derivative measures the rate of change of a function with respect to a variable.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the product rule for differentiation?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

Front

What is the chain rule for differentiation?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).