Implicit Differentiation

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, rather than explicitly solving for y.

Front

When is Implicit Differentiation used?

Back

Implicit differentiation is used when it is difficult or impossible to solve for y explicitly in terms of x.

Front

What is the derivative of sec(x)?

Back

The derivative of sec(x) is sec(x)tan(x).

Front

How do you apply the chain rule in differentiation?

Back

The chain rule states that if a function y is composed of another function u, then dy/dx = dy/du * du/dx.

Front

Find dy/dx if y = sec(8x^2).

Back

dy/dx = 16x sec(8x^2) tan(8x^2).

Front

What is the first step in implicit differentiation?

Back

The first step is to differentiate both sides of the equation with respect to x, applying the product rule and chain rule as necessary.

Front

Find dy/dx for the equation x + 4y = 1 using implicit differentiation.

Back

dy/dx = -1/4.

Front

What is the product rule in differentiation?

Back

The product rule states that if u and v are functions of x, then d(uv)/dx = u(dv/dx) + v(du/dx).

Front

Find dy/dx for the equation 9y + x = 4y using implicit differentiation.

Back

dy/dx = -1/5.

Front

What is the significance of the point (2,3) in the equation x^3 + 2xy - y^2 = 11?

Back

The point (2,3) is used to find the slope of the tangent line at that specific point after differentiating the equation.