5ADiffTrigFuns

__Derivatives of Trig Functions (from Methods)__

Derivative of Sine

See Maths Methods 07G

math \dfrac {d}{dx} \Big( sin(ax) \Big) = a \, \cos(ax) math

math \dfrac {d}{dx} \Big( \sin g(x) \Big) = g'(x) \, \cos g(x) math
 * Chain Rule Version**

Examples

Derviative of Cosine

See Maths Methods 07G

math \dfrac {d}{dx} \Big( \cos(ax) \Big) = -a \, \sin(ax) math

math \dfrac {d}{dx} \Big( \cos g(x) \Big) = -g'(x) \sin g(x) math
 * Chain Rule Version**

Derivative of Tangent

math \dfrac {d}{dx} \Big( \tan(ax) \Big) = a \, \sec^2(ax) math

math \dfrac {d}{dx} \Big( \tan g(x) \Big) = g'(x) \sec^2 g(x) math
 * Chain Rule Version**

**See also** [|www.mathsonline.com.au] Y12Advanced --> Trigonometry --> Trigonometric Functions --> Lesson 2

__Derivatives of Reciprocal Trig Functions (Specialist Only)__

The derivatives of reciprocal trig functions can be found using the Quotient Rule and the derivatives listed above.

Derivative of Cot

math \dfrac {d}{dx} \Big( \cot(ax) \Big) = -a \, \text {cosec}^2(ax) math

math \dfrac {d}{dx} \Big( \cot g(x) \Big) = -g'(x) \text {cosec}^2 g(x) math
 * Chain Rule Version**

Derivative of Sec

math \dfrac {d}{dx} \Big( \sec(ax) \Big) = a \, \sec(ax) \, \tan(ax) math

math \dfrac {d}{dx} \Big( \sec g(x) \Big) = g'(x) \sec g(x) \tan g(x) math
 * Chain Rule Version**

Derivative of Cosec

math \dfrac {d}{dx} \Big( \text{cosec } ax \Big) = -a \, \text{cosec }(ax) \, \cot(ax) math

math \dfrac {d}{dx} \Big( \text{cosec } g(x) \Big) = -g'(x) \text{cosec } g(x) \, \cot g(x) math
 * Chain Rule Version**

**See also** [|www.mathsonline.com.au] Y12Extension --> Trigonometry --> Further Trigonometry --> Lesson 9 .