Trig Derivatives

Front

What is the derivative of g(x) = sin^(1/2)(4x)?

Back

g'(x) = 2sin^(-1/2)(4x)cos(4x)

Front

If f(x) = sin^3(2x), what is f'(x)?

Back

f'(x) = 6sin^2(2x)cos(2x)

Front

Find the derivative of y = cot^4(x).

Back

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

Front

What is the derivative of y = cos^5(4x^3)?

Back

y' = -60x^2cos^4(4x^3)sin(4x^3)

Front

Find y' if y = tan(3x^2 + 2).

Back

y' = 6xsec^2(3x^2 + 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 product rule in differentiation?

Back

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

Front

What is the quotient rule in differentiation?

Back

The quotient rule states that if u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

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).