Chain Rule and Implicit Differentiation

Front

What does the term 'derivative' refer to in calculus?

Back

The derivative refers to the slope of the tangent line to a function at a given point.

Front

How do you find the derivative of a composite function?

Back

You use the chain rule.

Front

What is the formula for the chain rule in calculus?

Back

d(f(g(x)))/dx = f'(g(x)) * g'(x)

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y.

Front

How do you apply implicit differentiation to the equation 4x cos(y) = 1?

Back

Differentiate both sides with respect to x, treating y as a function of x, and solve for y'.

Front

What is the derivative of the function f(x) = xe^x?

Back

f'(x) = e^x + xe^x.

Front

What is the significance of the slope of the tangent line?

Back

It represents the instantaneous rate of change of the function at a specific point.

Front

What is a composite function?

Back

A composite function is a function formed by combining two functions, where the output of one function becomes the input of another.

Front

What is the relationship between the derivative and the slope of a function?

Back

The derivative at a point gives the slope of the tangent line to the function at that point.

Front

Can the chain rule be applied to functions of more than two variables?

Back

Yes, the chain rule can be extended to functions of multiple variables.