dy/dx
Definition
The derivative of a function y with respect to x, representing the rate of change of y with respect to x.
Analogy
Think of dy/dx as the speedometer in a car. It tells you how fast your position (y) is changing with respect to time (x). Just like how the speedometer shows your speed, dy/dx shows the rate at which y is changing.
Related terms
Tangent line: A line that touches a curve at only one point and has the same slope as the curve at that point.
Chain rule: A rule used to find the derivative of composite functions.
Implicit differentiation: A technique used to find derivatives when an equation involves both x and y variables.
"dy/dx" appears in:
Practice Questions (20+)
- To find dy/dx for an implicit relation, we differentiate both sides of the equation with respect to:
- If dy/dx = ysec^2x and y = 7 when x = 0, then y = ???
- FInd an equation for dy/dx=ky.
- Given the differential equation dy/dx = x^2 + y and the initial condition y(1) = 3, identify the initial x, initial y, and slope values for the first step of Euler's method.
- For the differential equation dy/dx - y = 1, which equation gives a value for the slope of the function y?
- Consider a differential equation dy/dx = 3x^2. What is the general solution for y(x)?
- Solve the initial value problem dy/dx = 2x, y(0) = 3.
- What is the general solution for the differential equation dy/dx = 4e^x?
- Solve the initial value problem dy/dx = 1/x, y(1) = 0.
- Find the general solution for the differential equation dy/dx = 2cos(x).
- Solve the initial value problem dy/dx = 1/(x^2), y(2) = 1/4.
- Given the differential equation: dy/dx = 2x + 3, find the particular solution for y(0) = 4.
- Solve the differential equation: dy/dx = 4e^x, given the initial condition y(0) = 1.
- Solve the differential equation: dy/dx = 2sin(x), given the initial condition y(0) = 0.
- Solve the differential equation: dy/dx = 5x^4, given the initial condition y(1) = 10.
- Given the differential equation: dy/dx = 3/x, find the particular solution for y(2) = 5.
- Solve the differential equation: dy/dx = 1/x^2, given the initial condition y(1) = 2.
- Which of the following represents the solution to the differential equation dy/dx = 0.02y?
- The solution to the differential equation dy/dx = 5y with an initial condition y(0) = 2 is given by:
- Which of the following represents the general solution to the differential equation dy/dx = -2y?
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