Calculus Product Rule Derivatives

Front

What is the Product Rule in calculus?

Back

The Product Rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: (u*v)' = u'v + uv'.

Front

Calculate the derivative of f(x) = -25xcos(x).

Back

f'(x) = 25xsin(x) - 25cos(x).

Front

Calculate the derivative of f(x) = x^2 cos(x) + 10x^2.

Back

f'(x) = -x^2sin(x) + 2xcos(x) + 20x.

Front

Calculate the derivative of f(x) = 2x^3 sin(x).

Back

f'(x) = 2x^3cos(x) + 6x^2sin(x).

Front

Find the derivative of f(x) = -7sin(x)cos(x).

Back

f'(x) = 7sin^2(x) - 7cos^2(x).

Front

Find the derivative of f(x) = 8sin^2(x).

Back

f'(x) = 16sin(x)cos(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 chain rule in calculus?

Back

The Chain Rule states that if you have a composite function f(g(x)), the derivative is f'(g(x)) * g'(x).

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.