Can 2 functions have same derivative?

Yes, two different functions can have the same derivative under certain conditions.

Can you have two distinct functions with the same anti derivative explain?

A(x) = B(x) + c on [a, b]. Thus any two antiderivative of the same function on any interval, can differ only by a constant. The antiderivative is therefore not unique, but is “unique up to a constant”.

What is the derivative of two functions?

“The derivative of a product of two functions is the first times the derivative of the second, plus the second times the derivative of the first.”

Can a function be equal to its derivative?

How many functions equal their own derivative?

one function
A derivative of the Exponential Function: We have only one function which is an exponential function whose derivative equals itself.

How many Antiderivatives can a function have?

Every continuous function has an antiderivative, and in fact has infinitely many antiderivatives. Two antiderivatives for the same function f(x) differ by a constant. To find all antiderivatives of f(x), find one anti-derivative and write “+ C” for the arbitrary constant.

Can two functions have the same integral?

No, because a function that contains a constant, such as f(x)=(x^5)-7 and a function that contains all the same terms yet has a different constant, (i.e. f(x)=(x^5)-6), will have the same indefinite integral, but are clearly not the same function.

How do you differentiate multiple functions?

The derivative of the product of two functions is the derivative of the first one multiplied by the second one plus the first one multiplied by the derivative of the second one. We can take that g ( x ) = x and h ( x ) = x and use the rule of the product.

Why is the derivative of E 2?

Explanation: The derivative is the measure of the rate of change of a function. Even though it may not look like a constant, like 4 or −12 , e2 still has a calculable value that never changes. Thus, the derivative of any constant, such as e2 , is 0 .

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.