Chain Rule and Implicit Differentiation

Front

What is the chain rule used for in calculus?

Back

Finding the derivative of a composite function.

Front

Find dy/dx at the given point: x^3 + 2xy - y^2 = 11 at (2,3)

Back

9

Front

Use implicit differentiation to find y' for the equation: 4x cos(y) = 1

Back

y' = cos(y) / (x sin(y))

Front

Find f '(x) if f(x) = x^4 sin(x)

Back

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

Front

Find dy/dx by Implicit Differentiation: x^3 + y^3 = 36

Back

dy/dx = -x^2 / y^2

Front

State the formula for the chain rule in differentiation.

Back

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

Front

What is implicit differentiation?

Back

A technique to find the derivative of a function defined implicitly by an equation.

Front

Differentiate the function: f(x) = (3x^2 + 2)^5

Back

f '(x) = 30x(3x^2 + 2)^4.

Front

What is the derivative of sin(g(x)) using the chain rule?

Back

The derivative is cos(g(x)) * g'(x).

Front

Find dy/dx for the equation: x^2 + y^2 = 25

Back

dy/dx = -x/y.