Differentiation- summary, Lecture notes of Mathematics

Download Differentiation- summary and more Lecture notes Mathematics in PDF only on Docsity!

even ID) f ferent ation, work out gradients” of graphs 4. Derivatives and gradient functions GS how steep? 4. Power rule graph “the derivate of d(x") + nn likewise, L 2 wit, > iB the derivative of 4lx) respect to is FQ) } ? eg. Par’ > gradient ee function. ge do ye et 2 - iz ate a. constant \ 4 Cree)] * k.4 CFI] | a. Scolar multiple rule du dx ye des det > dye 3.4 § Qaet = lane He de 7 ¥ 3. Addition/ a - 2rd) * S090 pommel) gel > ea” see + + 6 4. The chain rule eg: 4 = a u—~ du. ‘ dy dy x de ae Gude dus d (32-2) > 3 de de dy = du dy = 3 de. de de substitute. > alu back = al(3e-a). ay 2. Tongents and normals oe =a gradient ot pont ACH, y,) is me j, \angent _— tangent = touches eurve , doesn't go through A(X My) = same gradient os curve (m) ss. nota © cydiie qj tga normal ~ perpendicular hb to curve, + gradient: 4 m - equation of normal : -yoe -* (n- y- Ys + un) 3. Sexond derivatives first + affereniote. y with respect to x © dy ewatve = FG) dx second ——, a f'G) + differentiate cy with respect tox +d (# ) 2 derivative. dx Vax aa tgs yr xt Se- e td or FQ) = oot 5 - bn td Fi ’ dy + 32'+ On -3 or Fle) + tt oe -3 rd ) V dy + 6x + or Fle)» 6x + w de