Title: InkMaths / Differentiation: standard results
On every note of this deck, unless a note says otherwise:
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Front: STANDARD RESULT — LEARN IT
Natural log:
ddx(ln x) = ?
Back: ddx(ln x) = 1x

Front: STANDARD RESULT — LEARN IT
Sine (x in radians):
ddx(sin x) = ?
Back: ddx(sin x) = cos x

Front: STANDARD RESULT — LEARN IT
Power rule:
ddx(x^n) = ?
Back: ddx(x^n) = nx^n−1

Front: STANDARD RESULT — LEARN IT
Exponential:
ddx(e^kx) = ?
Back: ddx(e^kx) = ke^kx

Front: DEFINE
Define: differentiation from first principles.
Back: The derivative of f(x) is the limit as h tends to zero of (f(x + h) − f(x))/h, provided the limit exists.

Front: STANDARD RESULT — LEARN IT
Cosine (x in radians):
ddx(cos x) = ?
Back: ddx(cos x) = −sin x

Front: CHECK YOURSELF
Differentiate y = 3 ln x − cos 2x.
Back: dy/dx = 3/x + 2 sin 2x.
The 2 appears from the chain rule on cos 2x, and the sign flips because the derivative of cos is minus sin.

Front: SPOT THE ERROR
Say what is wrong with this claim:
The derivative of cos x is sin x.
Back: It is −sin x. Sine's derivative is cos x with no sign change; cosine's picks up the minus. Sketch both curves: cos x is falling just after zero, so its gradient there must be negative.

Front: STANDARD RESULT — LEARN IT
General exponential:
ddx(a^kx) = ?
Back: ddx(a^kx) = ka^kx ln a