Parallel lines will have the same slope, so we need to find the equation of each tangent line, identify their slopes, and then set the slopes equal to one another in order to find the value that makes them parallel.

The tangent line of a function at a point is the line which is tangent to the function at the point, meaning that it only intersects the line at a single point there. The slope of the tangent line at a point is the slope of the function at that point.

Sometimes it's easier to find the derivative of a function if you take the natural log of both sides of the equation first, and then use implicit differentiation to take the derivative. This process is called logarithmic differentiation.

Sometimes it's easier to find the derivative of a function if you take the natural log of both sides of the equation first, and then use implicit differentiation to take the derivative. This process is called logarithmic differentiation.

The derivative of the natural log function ln(x) is just 1/x. If the value inside the log is more complicated than just x, we'll have to apply chain rule and multiply by the derivative of that inside function in order to find the derivative of the log function.

The derivative of the natural log function ln(x) is just 1/x. If the value inside the log is more complicated than just x, we'll have to apply chain rule and multiply by the derivative of that inside function in order to find the derivative of the log function.

The derivative of e^(ax) is ae^(ax). In this video we'll apply that formula and the product and chain rules in order to find the derivative of the product of two functions, one of which is an exponential function.

This video explains how to find the equation of the tangent line to a curve, when that curve is defined by a function that can't be solved for y in terms of x. We'll use implicit differentiation to find the slope of the tangent line.

With normal differentiation, we take the derivative with respect to one variable only, usually x. With implicit differentiation, we take the derivative with respect to both x and y. Whenever we take the derivative with respect to y, we have to remember to multiply by y', or dy/dx. Implicit differentiation is important because it lets us take the derivative of any equation that can't be solved for y in terms of x.

This is an example of how to find the derivative of hyperbolic sine, using the formula for its derivative, and chain rule.