Derivatives #2: Trig Derivatives with the Chain Rule

Front

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

Back

The derivative is dy/dx = -5cos^4(x)sin(x). This uses the chain rule.

Front

What is the derivative of sec(x)?

Back

The derivative is d/dx[sec(x)] = sec(x)tan(x).

Front

How do you find the equation of the tangent line at a given point?

Back

To find the equation of the tangent line, use the point-slope form: y - y1 = m(x - x1), where m is the derivative at that point.

Front

What is the derivative of y = tan(3x^2 + 2)?

Back

The derivative is dy/dx = 6xsec^2(3x^2 + 2). This applies the chain rule.

Front

What is the derivative of f(x) = (x^2 + 2x)^5?

Back

The derivative is f'(x) = 5(x^2 + 2x)^4(2x + 2). This uses the chain rule.

Front

What is the chain rule in differentiation?

Back

The chain rule states that if you have a composite function y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).

Front

What is the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the derivative of tan(x)?

Back

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

Front

What is the product rule in differentiation?

Back

The product rule states that if you have two functions u(x) and v(x), then d/dx[uv] = u'v + uv'.