Chain Rule and Implicit Differentiation

Front

What is the general formula for the chain rule in calculus?

Back

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

Front

Find the derivative of the function f(x) = x^3 + x^2 + 3.

Back

3x^2 + 2x

Front

Differentiate the function y = ln(2x + 1) using the chain rule.

Back

2/(2x + 1)

Front

Find dy/dx by Implicit Differentiation for the equation x^3 + y^3 = 36.

Back

−x^2/y^2

Front

What is implicit differentiation used for in calculus?

Back

To find the derivative of an equation that is not explicitly expressed in terms of one variable.

Front

State the product rule for differentiation.

Back

If u and v are functions of x, then d(uv)/dx = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u and v are functions of x, then d(u/v)/dx = (u'v - uv')/v^2.

Front

Differentiate the function y = e^(3x).

Back

3e^(3x)

Front

What is the derivative of sin(x)?

Back

cos(x)

Front

What is the derivative of cos(x)?

Back

-sin(x)