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Computing Derivatives

Computing Derivatives

Example 1

  • z = ln(x5 + 4x2)

Example 2

  • z = (sin x + cos x)7

Example 3

Example 4

  • z = e{12x + 4}

Example 5

Example 6

For the pair of functions, determine what the chain rule says.

  • Let p = f(s) and s = g(z).

Example 7

For the pair of functions, determine what the chain rule says.

  • Let r = g(t) and q = f(r).

Example 8

For the pair of functions, determine what the chain rule says.

  • Let x = f(y) and y = g(z).

Example 9

  • If u = es and s = 5 - 3x2, find .

Example 10

  • If s = t4 and t = r4 + 1, find .

Example 11

  • If m = sin n and z = ln m, find .

Example 12

  • If z = (x4 + 4x) and y = z3 + z5, find .

Example 13

  • If  and q = tan p, find .

Example 14

  • Find given that r = sin(x2 + 1) + cos(x2 + 1).

Example 15

  • Find  given that p = e{r2 + 3r}

Example 16

  • Find  given that y = ln(z4 + z3)

Example 17

  • Find  given that  

Example 18

  • Find  given that q = 14{12sin t}.
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