SkipCaptcha
1,279
edits
Changes
Jump to navigation
Jump to search
Line 7:
Line 7: + + + + + + + + + + + + + + + + + + + + + + +
Added an example of using the product rule
The product rule in words is the derivative of uv is u multiplied by the derivative of v plus the derivative of u multiplied by v. The [[commutative property]] allows the terms to be interchanged, which occasionally leads to introduction in reverse.
The product rule in words is the derivative of uv is u multiplied by the derivative of v plus the derivative of u multiplied by v. The [[commutative property]] allows the terms to be interchanged, which occasionally leads to introduction in reverse.
==Example==
Let f(x) be the [[function]]:
<math>
f(x) = 3x \sin{5x}
</math>
To find its derivative, we split f(x) in two and apply the product rule with u equal 3x and v equal to the [[sine]] term:
<math>
f'(x) = 3 \times \sin{5x} + 3x \times (5\cos{5x}) = 3\sin{5x} + 15x \cos{5x}
</math>
==Rules for finding derivatives==
*[[Power rule]]
*[[Constant-multiple rule]]
*[[sum rule]]
*[[Chain rule]]
*[[Product rule]]
*[[Quotient rule]]
[[Category:Calculus]]
[[Category:Calculus]]
[[Category:Mathematics]]
[[Category:Mathematics]]
[[Category:Differentiation]]