# Implicit derivative of y = cos(5x - 3y) | Taking derivatives | Differential Calculus | Khan Academy | Summary and Q&A

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January 30, 2013
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Implicit derivative of y = cos(5x - 3y) | Taking derivatives | Differential Calculus | Khan Academy

## TL;DR

This video explains how to find the rate of change of a function using implicit differentiation.

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### Q: What does the derivative of the cosine function with respect to its argument equal?

The derivative of the cosine function with respect to its argument is equal to negative sine of that argument.

### Q: How do you differentiate the term -3y with respect to x?

To differentiate -3y with respect to x, you multiply the constant -3 by the derivative dy/dx of y with respect to x.

### Q: What is the general approach for solving implicit differentiation problems?

The general approach for solving implicit differentiation problems is to apply the derivative operator to both sides of the equation and then use algebraic manipulation to isolate the derivative of interest.

### Q: How do you find dy/dx in implicit differentiation?

To find dy/dx in implicit differentiation, algebraically rearrange the equation to isolate dy/dx on one side and then divide by the remaining terms.

## Summary & Key Takeaways

• The video demonstrates how to find the rate of change of a function by applying the derivative operator to both sides of an equation.

• The chain rule is then used to differentiate the cosine function, and the derivatives of the variables are computed.

• By rearranging the equation and solving for the rate of change, the video concludes with the expression dy/dx.