Solution - Derivative

\frac{\frac{d}{d x} [a] \times x - a}{x^{2}}

\frac{\frac{d}{dx}[a]\times x- a}{x^{2}}

See steps

Step-by-step explanation

1. Solve derivative

Computing the derivative of a fraction.

$\frac{d}{d x} [\frac{a}{x}] = \frac{\frac{d}{d x} [a] \times x - a \times \frac{d}{d x} [x]}{x^{2}}$

The derivative of a variable with respect to itself is always equal to one.

$\frac{\frac{d}{d x} [a] \times x - a \times \frac{d}{d x} [x]}{x^{2}} = \frac{\frac{d}{d x} [a] \times x - a \times 1}{x^{2}}$

Multiplying a number by one, which does not change its value.

$\frac{\frac{d}{d x} [a] \times x - a \times 1}{x^{2}} = \frac{\frac{d}{d x} [a] \times x - a}{x^{2}}$

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Why learn this

Ever wondered how to predict the future? Derivatives are your crystal ball!

Picture this: You're a surfer trying to catch the biggest wave. How do you know when it's coming? Derivatives can tell you when it's at its highest point!

Rocket Science: Planning to launch a rocket to Mars? Derivatives tell us the optimal fuel burn rate to minimize fuel consumption and maximize distance!

Stock Market: Trading in the stock market? Derivatives can indicate the rate at which stock prices are changing, helping predict the best time to buy or sell.

Animation: Love animated movies? Artists use derivatives to smoothly change the motion and expressions of characters, making them feel more lifelike.

Engineering: Designing a bridge or a skyscraper? Derivatives help determine the rates of stress and strain changes in materials, ensuring the safety of your structures.

In short, derivatives are like a secret code to understanding change and making predictions in real life. So let's crack this code together and become masters of our futures!

Terms and topics

Derivative

Solution - Derivative

Step-by-step explanation

1. Solve derivative

Why learn this

Terms and topics

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