# Laplace Transforms Of The Derivatives

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**Laplace Transforms of the Derivatives:**

If the Laplace Transform of f(t) is known then by using the following results we can find the Laplace transform of the derivatives;

**Laplace Transform of the derivatives:** Function of exponential order. A continuous function f(t), t > 0 is said to be of exponential order.

**Theorem:** If f(t) is exponential order and f' (t) is continuous then;

**Proof:** By the definition of Laplace Transform:

If f (t) = y then (4) can be written in the form:

Where y' , y'' , ......... y^{(n)} denoted the sucessive derivatives.