Angles must be in radians. d dxsin x=cos x d dxcos x=-sin x d dxtan x=sec2x x 0 Differentiate the angle as well as the outer trigonometric function. Example Differentiate cos(7x) with respect to x. ddxcos(7x) =-sin(7x). 7 =-7sin(7x) Differentiate tan(5x) with respect to x. ddxtan(5x) =sec2(5x). 5 =5sec2(5x) Differentiate sin(1-3x) with respect to x. ddxsin(1-3x) =cos(1-3x). (-3) =-3cos(1-3x)

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

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

Differentiate the angle as well as the outer trigonometric function.

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 \(x\).

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

Derivatives of Trigonometric Functions

Derivatives of Trigonometric Functions