Trig Derivatives (Delehant)

Front

What is the derivative of f(x) = x^4 cos(x)?

Back

f'(x) = x^4 cos(x) + 4x^3 sin(x)

Front

What is the derivative of f(x) = x^2 sin(x)?

Back

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

Front

What is the derivative of f(x) = tan(x) cos(x)?

Back

f'(x) = sec^2(x) cos(x) - tan(x) sin(x)

Front

What does it mean to take the derivative of a function?

Back

It means finding the slope of the tangent line to the function at a given point.

Front

What is the product rule for derivatives?

Back

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

Front

What is the chain rule for derivatives?

Back

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

Back

The derivative of cos(x) is -sin(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 x^n?

Back

The derivative of x^n is n*x^(n-1).