# If {eq}\displaystyle F(x) = \int_{25}^{x} \frac{1}{t} \ dt {/eq}, then find {eq}\displaystyle F'(x) {/eq}

## Question:

If {eq}\displaystyle F(x) = \int_{25}^{x} \frac{1}{t} \ dt {/eq}, then find {eq}\displaystyle F'(x) {/eq}

## Leibniz's Rule:

It is a special method used to find the derivative of a definite integral without integration. If the definite integral is {eq}\displaystyle \int\limits_{A\left( x \right)}^{B\left( x \right)} {f\left( x \right)} dx {/eq}, then the following formula can be used to find the derivative of the definite integral.

{eq}\displaystyle \dfrac{d}{{dx}}\int\limits_{A\left( x \right)}^{B\left( x \right)} {f\left( x \right)} dx = f\left[ {B\left( x \right)} \right]\dfrac{d}{{dx}}B\left( x \right) - f\left[ {A\left( x \right)} \right]\dfrac{d}{{dx}}A\left( x \right) {/eq}

The above formula is known as Leibniz's formula.

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Given Data

• The given definite integral is {eq}\displaystyle F(x) = \int\limits_{25}^x {\dfrac{1}{t}} \;dt {/eq}.

Using the Leibniz's rule to...