Implicit Differentiation

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to differentiate equations that define y implicitly in terms of x, rather than explicitly solving for y.

Front

How do you find dy/dx using implicit differentiation?

Back

To find dy/dx using implicit differentiation, differentiate both sides of the equation with respect to x, applying the chain rule to terms involving y, and then solve for dy/dx.

Front

What is the derivative of y^2 with respect to x?

Back

The derivative of y^2 with respect to x is 2y(dy/dx) due to the chain rule.

Front

What is the slope of the tangent line to a curve at a point?

Back

The slope of the tangent line to a curve at a point is given by the value of dy/dx at that point.

Front

How do you find the equation of a tangent line using implicit differentiation?

Back

To find the equation of a tangent line, first find dy/dx at the given point, then use the point-slope form of the line: y - y1 = m(x - x1), where m is the slope.

Front

What is the point-slope form of a line?

Back

The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

If x^2 + xy = 10, what is dy/dx when x = 2?

Back

When x = 2, dy/dx = -7/2.

Front

What is the derivative of x^2 with respect to x?

Back

The derivative of x^2 with respect to x is 2x.

Front

How do you differentiate a product of two functions, such as xy?

Back

Use the product rule: d(uv)/dx = u(dv/dx) + v(du/dx), where u = x and v = y.

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.