Question

If a function y = f(x) satisfies \frac{dy}{dx} = y, then y= e^{x}.

Select one:
True
False

Answer 1

$y = f(x)$ satisfies $\frac{dy}{dx} = y$, then $y= e^{x}$. It is true.

Method for finding the Derivative of a function is Differentiation.

Derivative is the method to find out how a function $y = f(x)$ is changing whenever the input (i.e. value of x) is changed.

$y = f(x)$ means y is a function of x.  

Whenever there is a change in value of 'x', the value of 'y' also gets changed.

For finding the rate of change of 'y' we use derivative.

Derivative of $y = f(x)$ can be represented as $\frac{dy}{dx}\ or\ f'(x)$.

Derivative of $e^x$ is always equal to $e^x$.

Graph of $e^x$ is attached hereby.

Hence, if $y = f(x)$ satisfies $\frac{dy}{dx} = y$, then $y= e^{x}$. It is TRUE.