2.7 Derivatives of sin, cos, e^x, ln x

Trig

Memorize: d/dx[sin x] = cos x and d/dx[cos x] = −sin x. (Cosine's derivative carries the negative sign.)

Exponential & log

d/dx[e^x] = e^x — e^x is its own derivative — and d/dx[ln x] = 1/x.

Key terms

d/dx sin x

= cos x.

d/dx cos x

= −sin x (note the negative).

d/dx e^x

= e^x (its own derivative).

d/dx ln x

= 1/x.

Self-derivative

e^x is the function equal to its own derivative.

Try an AP-style question

d/dx (3 sin x − 2 cos x) = ?

1. 3 cos x − 2 sin x
2. 3 cos x + 2 cos x
3. 3 cos x + 2 sin x
4. −3 cos x + 2 sin x