Chapter 2: Differentiation
Section 2.7: Derivatives of the Trig Functions
Evaluate ⅆⅆx sinxtanx2.
Control-drag the differentiation problem.
Press the Enter key.
Context Panel: Simplify≻Simplify
Context Panel: Expand≻Expand
(At one time, Maple's Smart Pop-Up applied to tan2x2 sufficed to convert the derivative into the form obtained in Table 2.7.3(a). At the present time, further progress towards this goal requires the application of commands.)
The Maple derivative for tanx is 1+tan2x, and not the equivalent sec2x. Fortunately, Maple simplifies tan2x2 to sec2x2−1. The stepwise evaluation of the derivative in Table 2.7.3(a) starts with the Product rule, but uses the Chain rule to differentiate one of the factors.
=2 x sinx sec2x2+cosx tanx2
Table 2.7.3(a) Stepwise evaluation of the derivative of sinxtanx2
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