5/12 Review 2_Chain Rule, Derivatives, and Implicit Differe.

Front

What is the Chain Rule in calculus?

Back

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. It states that if you have two functions f(x) and g(x), then the derivative of their composition f(g(x)) is f'(g(x)) * g'(x).

Front

How do you find the first derivative of a function?

Back

To find the first derivative of a function, apply the rules of differentiation (such as the power rule, product rule, quotient rule, and chain rule) to determine the rate of change of the function with respect to its variable.

Front

What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, where n is a real number, then the derivative f'(x) = n*x^(n-1).

Front

How do you find the second derivative of a function?

Back

To find the second derivative of a function, first find the first derivative, and then differentiate that result again with respect to the variable.

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to differentiate equations that define y implicitly in terms of x, rather than explicitly as y = f(x). It involves differentiating both sides of the equation with respect to x and applying the chain rule.

Front

What is the derivative of sin(x)?

Back

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

Front

What is the derivative of e^(x)?

Back

The derivative of e^(x) is e^(x).

Front

How do you differentiate a function of the form y = sin(g(x))?

Back

To differentiate y = sin(g(x)), use the chain rule: y' = cos(g(x)) * g'(x).

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero.

Front

What is the product rule for differentiation?

Back

The product rule states that if you have two functions u(x) and v(x), then the derivative of their product is (u*v)' = u'v + uv'.