diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index 7c460c3..d693351 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -531,6 +531,27 @@ $$f´(x) = g´(h(x)) · h´(x)$$ $$f(x) = (4x^2-3x+1)^7$$ $$f´(x) = 7(4x^2-3x+1)^6 (8x-3)$$ +### Trigonometric derivative rules + +$$ +\frac{d}{dx}\sin x = \cos x \\ +\frac{d}{dx}\cos x = -\sin x \\ +$$ + +These primary derived rules can be used to further derive the derivatives of the other trignometric ratios: +$$ +\frac{d}{dx}\tan x = \sec^2 x \\ +\frac{d}{dx}\csc x = -\csc x\cdot\cot x \\ +\frac{d}{dx}\sec x = \sec x\cdot\tan x +$$ + +The **chain rule** applies to trigonometric functions and will be applied recursively if needed. + +!!! example + $$\frac{d}{dx}[\sin g(x)]^n = n[\sin g(x)]^{n-1}\cdot\cos x\cdot g´(x)$$ + +Trigonometric identities are not polynomial so values on an interval need to be determined by substituting values between vertical asymptotes and critical points. + ### Higher order derivatives The **second derivative** of $f(x)$ is the derivative of the first derivative of $f(x)$, that is, $f´´(x)$.