# Differentiating using Calculator Trick with Definite Derivative

Differentiate $y=sec^2(x)$

Answer in Problem Set: $2x\cdot sec^2(x)\cdot tan^2(x)$

Answer in Wolfram Alpha: $2 \cdot tan(x) \cdot sec^2(x)$

We can always solve it manually, deriving and stuff; but board exam has very limited time therefore we were told its always better to use shortcut. My Calculator, a Casio FX-991ES Plus can only evaluate Definite Derivatives but not give me the answer straightforward.

So I try:

d/dx ((2*x)*(sec^2(x))*(tan^2(x)))


with $x = 2.5$ radians and I get a the derivative of

-2.327784695


Then when I use the correct answer from the problem set

(2*x)*(sec^2(x))*(tan^2(x))


and plug in $x = 2.5$, I get a different answer:

4.347267676...


How can that be? Isn't that supposed to be the slope? How can I avoid this problem?

• This is what you get from WA's answer evaluated at $x = 2.5$ though; I wouldn't trust the answer in the problem set. – pjs36 Jun 12 '15 at 1:40
• Don't know about you, but it would take me about $3$ seconds to find the derivative "manually", and probably about $30$ seconds to do all that evaluation stuff. Why not just learn to differentiate instead of playing the "exam game"? BTW the given answer is wrong. – David Jun 12 '15 at 1:42
• The point remains that in this case I would have been $10$ times slower doing it your way. Maybe it's different for you. Anyway, it's your exam not mine so never mind. – David Jun 12 '15 at 1:59
• Rather than the phrase "definite derivative" I think you mean "numeric derivative." – Rory Daulton Jun 12 '15 at 8:45
• Are we sure we aren't talking about $\sec(x^2)$? That has derivative $2x\sec(x^2)\tan(x^2)$ which is the answer in the problem set, if you just misinterpret or typo the ^2. – Gerry Myerson Jul 25 '15 at 0:21