Derivatives of Trigonometric Functions - Introduction
By now, you should have seen the derivatives of basic functions such as polynomials. We will now start exploring the derivatives of trigonometric functions. First, let us list the rules:
.
First, we start with the left hand side of the equation:
dxdtanx
By the trigonometric identity of
tanx=cosxsinx
, we have:
dxdtanx=dxdcosxsinx
Then, we apply the quotient rule:
dxdtanx=cos2xcosxcosx−sinx(−sinx)
Simplify:
dxdtanx=cos2xcos2x+sin2x
Apply the trigonometric identity of
cos2x+sin2x=1
:
dxdtanx=cos2x1
Apply the trigonometric identity of
cosx1=secx
:
dxdtanx=sec2x
We are done. We have shown that the left hand side equals the right hand side, and that the derivative of
tanx
is indeed
sec2x
.
What's Next
A good way to get better at finding derivatives for trigonometric functions is more practice! You can try out more practice problems at the top of this page. Once you are familiar with this topic, you can also try other practice problems. Soon, you will find all derivatives problems easy to solve.
At Cymath, we believe that sufficient practice and step-by-step guidance can help students master most differentiation and integration problems. You can try our online solver anytime, or download the Cymath homework helper app for iOS and Android today!