What is the Derivative of -sinx?

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SUMMARY

The derivative of -sin(x) is definitively cos(x). This conclusion is based on the rule that the derivative of sin(x) is cos(x), and since -1 is a constant multiplier, it can be factored out during differentiation. Therefore, the derivative can be expressed as d/dx((-1)(sin(x))) = (-1)(cos(x)). Understanding this concept relies on the linearity of differentiation.

PREREQUISITES
  • Basic understanding of calculus and differentiation
  • Familiarity with trigonometric functions, specifically sin(x) and cos(x)
  • Knowledge of constant multiples in differentiation
  • Understanding of the linearity property of derivatives
NEXT STEPS
  • Study the rules of differentiation, focusing on constant multiples
  • Learn about the derivatives of other trigonometric functions
  • Explore the concept of linearity in calculus
  • Review the Wikipedia page on the Table of Derivatives for comprehensive examples
USEFUL FOR

Students of calculus, mathematics educators, and anyone seeking to deepen their understanding of differentiation in trigonometric functions.

Sakha
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I know the derivative of cos(x) = -sinx
is the derivative of -sinx= cosx
or maybe derivative of -sinx = 1/cosx
which is it
 
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Derivative of sin(x) is cos(x).
Derivative of (-1)*(sin(x))= (-1) (cos(x))
The - is just a constant you can take out front.
 
Thanks i got it
 
Last edited:
With respect to some variable, the derivative of a constant is zero. However by recognizing (-1) as a constant multiple while taking the derivative of a function of a variable with respect to that variable, you can write:
d/dx((-1)(f(x))= (-1) d/dx(f(x)) = (-1) (f'(x)

Edit: http://en.wikipedia.org/wiki/Table_of_derivatives
See: Linearity
 

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