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Solution - Derivative

cos(x)sin(x)
\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}

Other Ways to Solve

Derivative

Step-by-step explanation

1. Solve derivative

2 additional steps

Computing the derivative of a logarithm function using the chain rule.

ddx[ln(sin(x))]=1sin(x)×ddx[sin(x)]

Decomposing the function for the chain rule.

ddx[ln(sin(x))]=ddx[ln(x)]×ddx[sin(x)]

Computing the derivative of a natural logarithm function.

ddx[ln(x)]×ddx[sin(x)]=1x×ddx[sin(x)]

Substituting the variable back into the function.

1x×ddx[sin(x)]=1sin(x)×ddx[sin(x)]

Computing the derivative of a sine function.

1sin(x)×ddx[sin(x)]=1sin(x)×cos(x)

Simplifying the arithmetic expressions.

1sin(x)×cos(x)=cos(x)sin(x)

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!

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