Measure the Slopes and These Four Results Draw Themselves

You'll learnthe derivatives of sine, cosine, eˣ and ln x by reading them off their own graphs, which of the trig pair carries the minus sign, and why only base e is its own slope.

Four functions no algebraic rule reaches. Instead of quoting their derivatives, this animation measures the slope of each curve point by point and lets you watch which familiar curve the measurements draw. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · THE MINUS SIGN LIVES ON THE COSINE'S DERIVATIVE · RADIANS ONLY · v2

sin x → cos x · eˣ → eˣ · ln x → 1 / x

Before you start

What you're looking at

One period of sin x. A tangent is about to ride along it, and its slope will be measured at every point.

The question

When those measured slopes are joined up, which curve do they draw, and where does the minus sign that separates sine from cosine come from?

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