What function has a derivative equal to itself?

exponential function
The derivative of an exponential function is a constant times itself. Using this definition, we see that the function has the following truly remarkable property. Hence is its own derivative. In other words, the slope of the plot of is the same as its height, or the same as its second coordinate.

Can 2 functions have the same derivative?

If two functions have the same derivative, then the tangent lines at corresponding points should have the same slopes, or to put it another way, their graphs should go up and down in the same way. If the two graphs also share a point and they are parallel, then they must be the same.

What is the derivative equal to?

The Definition of Differentiation The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point.

Is e x the only function that is its own derivative?

In fact, ex (including its multiples cex) is the only function that is its own derivative. So, if you were told to find a function f(x) where f′(x)=f(x), you’d know that the function must be f(x)=cex for some (unknown) number c.

Can two functions have the same gradient?

We know that derivative of a function at a given point is the slope of the graph of that function at that point. If the two functions are to have same derivatives at all points in the interval, their graphs will have to have the same slope everywhere in the interval.

What is the meaning of derivative of a function?

derivative, in mathematics, the rate of change of a function with respect to a variable. Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point.

How do you find the gradient of two functions?

To find the gradient, take the derivative of the function with respect to x , then substitute the x-coordinate of the point of interest in for the x values in the derivative.

How do you know if two functions are tangent?

The slope of the tangent line will be given by inserting a point x=a into the derivative. Hence, it makes sense to start by finding the derivative of each function. Let f(x)=x3−3x+4 and g(x)=3×2−3x . So, the functions will share tangent lines at the points x=0 and x=2 .