Extreme calculus tutorial on how to take the derivative. Learn all the differentiation techniques you need for your calculus 1 class, including product rule, quotient rule, chain rule, logarithmic differentation, implicit differentiation, definition of derivative, and more!
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0:00 100 calculus derivatives
Big thanks to Mark Vinci for the time stamps:
Q1,
3:51, d/dx ax^+bx+c
Q2,
5:18, d/dx sinx/(1+cosx)
Q3,
8:31, d/dx (1+cosx)/sinx
Q4,
11:21, d/dx sqrt(3x+1)
Q5,
13:19, d/dx sin^3(x)+sin(x^3)
Q6,
16:48, d/dx 1/x^4
Q7,
18:53, d/dx (1+cotx)^3
Q8,
21:03, d/dx x^2(2x^3+1)^10
Q9,
28:39, d/dx x/(x^2+1)^2
Q10,
34:37, d/dx 20/(1+5e^-2x)
Q11,
38:10, d/dx sqrt(e^x)+e^sqrt(x)
Q12,
41:27, d/dx sec^3(2x)
Q13,
43:57, d/dx 1/2 (secx)(tanx) + 1/2 ln(secx + tanx)
Q14,
52:31, d/dx (xe^x)/(1+e^x)
Q15,
56:26, d/dx (e^4x)(cos(x/2))
Q16,
1:00:05, d/dx 1/4th root(x^3 - 2)
Q17,
1:04:04, d/dx arctan(sqrt(x^2-1))
Q18,
1:07:31, d/dx (lnx)/x^3
Q19,
1:10:25, d/dx x^x
Q20,
1:14:46, dy/dx for x^3+y^3=6xy
Q21,
1:21:35, dy/dx for ysiny = xsinx
Q22,
1:24:22, dy/dx for ln(x/y) = e^(xy^3)
Q23,
1:30:45, dy/dx for x=sec(y)
Q24,
1:35:59, dy/dx for (x-y)^2 = sinx + siny
Q25,
1:40:16, dy/dx for x^y = y^x
Q26,
1:46:31, dy/dx for arctan(x^2y) = x+y^3
Q27,
1:54:43, dy/dx for x^2/(x^2-y^2) = 3y
Q28,
1:58:03, dy/dx for e^(x/y) = x + y^2
Q29,
2:03:46, dy/dx for (x^2 + y^2 – 1)^3 = y
Q30,
2:06:51, d^2y/dx^2 for 9x^2 + y^2 = 9
Q31,
2:17:01, d^2/dx^2(1/9 sec(3x))
Q32,
2:21:35, d^2/dx^2 (x+1)/sqrt(x)
Q33,
2:26:33, d^2/dx^2 arcsin(x^2)
Q34,
2:32:04, d^2/dx^2 1/(1+cosx)
Q35,
2:36:57, d^2/dx^2 (x)arctan(x)
Q36,
2:39:49, d^2/dx^2 x^4 lnx
Q37,
2:42:34, d^2/dx^2 e^(-x^2)
Q38,
2:45:02, d^2/dx^2 cos(lnx)
Q39,
2:47:44, d^2/dx^2 ln(cosx)
Q40,
2:48:52, d/dx sqrt(1-x^2) + (x)(arcsinx)
Q41,
2:51:48, d/dx (x)sqrt(4-x^2)
Q42,
2:54:34, d/dx sqrt(x^2-1)/x
Q43,
2:56:34, d/dx x/sqrt(x^2-1)
Q44,
2:59:03, d/dx cos(arcsinx)
Q45,
2:59:56, d/dx ln(x^2 + 3x + 5)
Q46,
3:01:24, d/dx (arctan(4x))^2
Q47,
3:03:35, d/dx cubert(x^2)
Q48,
3:04:50, d/dx sin(sqrt(x) lnx)
Q49,
3:07:56, d/dx csc(x^2)
Q50,
3:08:50, d/dx (x^2-1)/lnx
Q51,
3:11:16, d/dx 10^x
Q52,
3:13:08, d/dx cubert(x+(lnx)^2)
Q53,
3:17:07, d/dx x^(3/4) – 2x^(1/4)
Q54,
3:19:54, d/dx log(base 2, (x sqrt(1+x^2))
Q55,
3:26:39, d/dx (x-1)/(x^2-x+1)
Q56,
3:29:28, d/dx 1/3 cos^3x – cosx
Q57,
3:32:08, d/dx e^(xcosx)
Q58,
3:33:55, d/dx (x-sqrt(x))(x+sqrt(x))
Q59,
3:34:40, d/dx arccot(1/x)
Q60,
3:37:50, d/dx (x)(arctanx) – ln(sqrt(x^2+1))
Q61,
3:42:22, d/dx (x)(sqrt(1-x^2))/2 + (arcsinx)/2
Q62,
3:47:30, d/dx (sinx-cosx)(sinx+cosx)
Q63,
3:52:45, d/dx 4x^2(2x^3 – 5x^2)
Q64,
3:55:06, d/dx (sqrtx)(4-x^2)
Q65,
3:57:27, d/dx sqrt((1+x)/(1-x))
Q66,
4:01:40, d/dx sin(sinx)
Q67,
4:03:00, d/dx (1+e^2x)/(1-e^2x)
Q68,
4:06:18, d/dx [x/(1+lnx)]
Q69,
4:08:19, d/dx x^(x/lnx)
Q70,
4:10:04, d/dx ln[sqrt((x^2-1)/(x^2+1))]
Q71,
4:13:43, d/dx arctan(2x+3)
Q72,
4:15:55, d/dx cot^4(2x)
Q73,
4:17:47, d/dx (x^2)/(1+1/x)
Q74,
4:20:44, d/dx e^(x/(1+x^2))
Q75,
4:23:13, d/dx (arcsinx)^3
Q76,
4:24:42, d/dx 1/2 sec^2(x) – ln(secx)
Q77,
4:27:08, d/dx ln(ln(lnx)))
Q78,
4:28:51, d/dx pi^3
Q79,
4:34:04, d/dx ln[x+sqrt(1+x^2)]
Q80,
4:37:52, d/dx arcsinh(x)
Q81,
4:46:55, d/dx e^x sinhx
Q82,
4:48:38, d/dx sech(1/x)
Q83,
4:52:51, d/dx cosh(lnx))
Q84,
4:56:21, d/dx ln(coshx)
Q85,
4:57:36, d/dx sinhx/(1+coshx)
Q86,
5:00:35, d/dx arctanh(cosx)
Q87,
5:03:54, d/dx (x)(arctanhx)+ln(sqrt(1-x^2))
Q88,
5:07:23, d/dx arcsinh(tanx)
Q89,
5:10:39, d/dx arcsin(tanhx)
Q90,
5:12:32, d/dx (tanhx)/(1-x^2)
Q91,
5:14:58, d/dx x^3, definition of derivative
Q92,
5:20:41, d/dx sqrt(3x+1), definition of derivative
Q93,
5:26:16, d/dx 1/(2x+5), definition of derivative
Q94,
5:31:18, d/dx 1/x^2, definition of derivative
Q95,
5:35:34, d/dx sinx, definition of derivative
Q96,
5:44:06, d/dx secx, definition of derivative
Q97,
5:54:41, d/dx arcsinx, definition of derivative
Q98,
6:13:26, d/dx arctanx, definition of derivative
Q99,
6:18:35, d/dx f(x)g(x), definition of derivative
Q100, d/dx f(x)/g(x), definition of derivative
Q101, d/dx tetration of x (i.e. x^x^x)
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