IB AA SL: Core and Optional Content Core: Sine and cosine derivatives; tangent can be derived using

Question

IB AA SL: Core and Optional Content

Core: Sine and cosine derivatives; tangent can be derived using the quotient rule.
Optional: Reciprocal-trigonometric notation and any unintroduced reciprocal-function derivative formulae.

Angles must be in radians.

$\dfrac{\mathrm d}{\mathrm dx}\sin x=\cos x\qquad\dfrac{\mathrm d}{\mathrm dx}\cos x=-\sin x$

$\dfrac{\mathrm d}{\mathrm dx}\tan x=\sec^2x\qquad\cos x\ne0$

Differentiate the angle as well as the outer trigonometric function.

Example

Differentiate $\cos(7x)$ with respect to $x$.

$\dfrac{\mathrm{d}}{\mathrm{d}x}\cos(7x)$${}=-\sin(7x)\cdot7$${}=-7\sin(7x)$

Differentiate $\tan(5x)$ with respect to $x$.

$\dfrac{\mathrm{d}}{\mathrm{d}x}\tan(5x)$${}=\sec^2(5x)\cdot5$${}=5\sec^2(5x)$

Differentiate $\sin(1-3x)$ with respect to $x$.

$\dfrac{\mathrm{d}}{\mathrm{d}x}\sin(1-3x)$${}=\cos(1-3x)\cdot(-3)$${}=-3\cos(1-3x)$

Accepted Answer

$\frac{\mathrm{d}}{\mathrm{d}x}\cos(7x)=-7\sin(7x)$, $\frac{\mathrm{d}}{\mathrm{d}x}\tan(5x)=5\sec^2(5x)$, $\frac{\mathrm{d}}{\mathrm{d}x}\sin(1-3x)=-3\cos(1-3x)$

Basics of Trigonometric Derivative

Basics of Trigonometric Derivative

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