What is the general notation when differentiating both sides of an equation with respect to x?

$\frac{d}{dx}(\text{equation}) = \frac{d}{dx}(\text{other side})$

Flip to see [answer/question]

Revise later

SpaceTo flip

If confident

All Flashcards

What is the general notation when differentiating both sides of an equation with respect to x?

$\frac{d}{dx}(\text{equation}) = \frac{d}{dx}(\text{other side})$

What is the point-slope form of a tangent line equation?

$y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

State the product rule.

$\frac{d}{dx}(uv) = u\frac{dv}{dx} + v\frac{du}{dx}$

How to find $\frac{dy}{dx}$ using implicit differentiation?

Differentiate both sides with respect to $x$ . 2. Apply chain rule to y terms. 3. Isolate $\frac{dy}{dx}$ .

How to find the tangent line equation at a point?

Find $\frac{dy}{dx}$ at the point. 2. Use point-slope form: $y - y_1 = m(x - x_1)$ .

What is implicit differentiation?

A method to find derivatives when $y$ is not explicitly defined in terms of $x$ .

What is $\frac{dy}{dx}$ in implicit differentiation?

Represents the derivative of $y$ with respect to $x$ , found when $y$ is not explicitly defined.

All Flashcards

What is the general notation when differentiating both sides of an equation with respect to x?

$\frac{d}{dx}(\text{equation}) = \frac{d}{dx}(\text{other side})$

What is the point-slope form of a tangent line equation?

$y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

State the product rule.

$\frac{d}{dx}(uv) = u\frac{dv}{dx} + v\frac{du}{dx}$

How to find $\frac{dy}{dx}$ using implicit differentiation?

Differentiate both sides with respect to $x$ . 2. Apply chain rule to y terms. 3. Isolate $\frac{dy}{dx}$ .

How to find the tangent line equation at a point?

Find $\frac{dy}{dx}$ at the point. 2. Use point-slope form: $y - y_1 = m(x - x_1)$ .

What is implicit differentiation?

A method to find derivatives when $y$ is not explicitly defined in terms of $x$ .

What is $\frac{dy}{dx}$ in implicit differentiation?

Represents the derivative of $y$ with respect to $x$ , found when $y$ is not explicitly defined.