Derivatives #2: Trig Derivatives with the Chain Rule

Front

What is the derivative of y = cot^4(x)?

Back

y' = -4cot^3(x)csc^2(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(5x^4)?

Back

f'(x) = -20x^3 sin(5x^4)

Front

What is the formula for the equation of a tangent line?

Back

y - f(a) = f'(a)(x - a) where (a, f(a)) is the point of tangency.

Front

Find the derivative of f(x) = (x^2 + 2x)^5.

Back

f'(x) = 5(x^2 + 2x)^4(2x + 2)

Front

What is the chain rule in differentiation?

Back

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

Front

What is the derivative of tan(x)?

Back

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

Front

What is the derivative of sec(x)?

Back

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

Front

What is the derivative of csc(x)?

Back

The derivative of csc(x) is -csc(x)cot(x).

Front

What is the derivative of sin(kx) where k is a constant?

Back

The derivative is kcos(kx).