NettetIf we accept that d/dx (cos x) = − sin x, and the power rule then: sec x ≡ 1/cos x Let u = cos x, thus du = − sin x dx sec x = 1/u (1/u) = (u⁻¹) By the power rule: derivative of (u⁻¹) = −u⁻² du Back substituting: = − (cos x)⁻² ( − sin x) ∙ dx = [sin x / (cos x)²] ∙ dx = [ (sin x / cos x) ∙ (1/cos x)] ∙ dx = [tan (x) ∙ sec (x)] ∙ dx 5 comments NettetSelesaikan soal matematika Anda menggunakan pemecah soal matematika gratis kami dengan solusi langkah demi langkah. Pemecah soal matematika kami mendukung matematika dasar, pra-ajabar, aljabar, trigonometri, kalkulus, dan lainnya.

Proving the derivatives of sin (x) and cos (x) - Khan Academy

Nettetsinx −cosx sinhx coshx cosx sinx coshx sinhx tanx −ln cosx tanhx lncoshx cosecx ln tan x 2 cosechx ln tanh x 2 secx ln secx+tanx sechx 2tan−1 ex sec2 x tanx sech2 x tanhx cotx ln sinx cothx ln sinhx sin2 x x 2 − sin2 x 4 sinh 2 x sinh2 4 − x 2 cos2 x x 2 + sin2 x 4 cosh 2 x sinh2 4 + x 2 Toc JJ II J I Back gift 7 year rule

Differentiation of trigonometric functions - Wikipedia

NettetIt's h (g (x)) because the integral (on the upper bound) approaches sin (x) and not x, and this makes it a composite function because h (x) = the integral but with x as the upper bound rather than sin (x) and g (x) = sin (x) which makes F (x) = h (g (x)) and F' (x) = h' (g (x)) * g' (x) by the chain rule. NettetDifferentiate algebraic and trigonometric equations, rate of change, stationary points, nature, curve sketching, and equation of tangent in Higher Maths. NettetYou can actually use the derivatives of sine and cosine (along with the quotient rule) to obtain the derivatives of all the other functions. Want to learn more about differentiating trigonometric functions? Check out this video about sine and cosine, this video about … gift999 163.com