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Find the derivative of the function. y = 6x^(-2) - 7x^(-1).

Question:

Find the derivative of the function.

{eq}y = 6x^{-2} - 7x^{-1} {/eq}

Calculus

The derivative is the tool of calculus, it is usually used to find the slope of the function. There are specified formulas and steps to solve different types of mathematical functions.

Answer and Explanation:

Given information

{eq}y = 6{x^{ - 2}} - 7{x^{ - 1}} {/eq}


The derivative of the above function can be calculated as follows.

{eq}\begin{align*} y &= 6{x^{ - 2}} - 7{x^{ - 1}}\\ \dfrac{{dy}}{{dx}} &= 6*\left( { - 2} \right){x^{ - 2 - 1}} - 7*\left( { - 1} \right){x^{ - 1 - 1}} \ \ \ \ \ \ {\rm{ }}\left( {{\rm{By \ using \ power \ rule: \ }}\dfrac{d}{{dx}}{x^n} = n{x^{n - 1}}{\rm{ }}} \right)\\ &= - 12{x^{ - 3}} + 7{x^{ - 2}} \end{align*} {/eq}


Learn more about this topic:

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The Fundamental Theorem of Calculus

from Math 104: Calculus

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