# Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =...

## Question:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

{eq}G(x) = \int_{x}^{2} \cos( \sqrt{7t} ) \, \mathrm{d}t {/eq}

## How to Find the Derivative Using the Fundamental Theorem of Calculus:

Finding the derivative of a function is a simple process, and when we calculate the derivative of a function using the Fundamental Theorem of Calculation it is even easier because this theorem considers the derivative as an inverse operation between derivatives and integrals. Part 1 of the Fundamental Theorem of Calculus is:

{eq}\eqalign{ & G(x) = \int_a^x {f(t)dt} \cr & \dot G(x) = \frac{d}{{dx}}\int_{a(x)}^{b(x)} {f(t)dt} \cr & \dot G(x) = f(b(x))*\dot b(x) - f(a(x))*\dot a(x) \cr} {/eq}

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{eq}\eqalign{ & {\text{We find the derivative using the Part 1 of the Fundamental Theorem of Calculus}}{\text{. Given }}G(x): \cr & G(x) = \int_x^2...