Section 1
Derivatives
By Boundless
![Thumbnail](../../../../../../figures.boundless-cdn.com/17891/raw/tangent-to-a-curve.jpg)
The use of differentiation makes it possible to solve the tangent line problem by finding the slope
![Thumbnail](../../../../../../figures.boundless-cdn.com/17890/raw/tangent-to-a-curve.jpg)
Differentiation is a way to calculate the rate of change of one variable with respect to another.
![Thumbnail](../../../../../../figures.boundless-cdn.com/31921/square/wvoesf0usqwdyjujjs7p.jpg)
If every point of a function has a derivative, there is a derivative function sending the point
![Thumbnail](../../../../../../figures.boundless-cdn.com/17914/square/800px-oracle-rocket.jpeg)
The rules of differentiation can simplify derivatives by eliminating the need for complicated limit calculations.
![Thumbnail](../../../../../../figures.boundless-cdn.com/31919/square/jtbrkp8t7sc83iilchnb.jpg)
Derivatives of trigonometric functions can be found using the standard derivative formula.
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The chain rule is a formula for computing the derivative of the composition of two or more functions.
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Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions.
Differentiation, in essence calculating the rate of change, is important in all quantitative sciences.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17919/square/fourcorner-relatedrates.jpg)
Related rates problems involve finding a rate by relating that quantity to other quantities whose rates of change are known.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17920/square/acceleration.jpeg)
The derivative of an already-differentiated expression is called a higher-order derivative.