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The Chain Rule in Leibniz Notation Exercises

Example 1

  • If z = ln(x5 + 4x2), then what is the derivative of z with respect to x?

Example 2

  • If z = (sin x + cos x)7 what is the derivative of z with respect to x?

Example 3

  • What is the derivative of z with respect to x if ?

Example 4

  •  If z = e12x + 4 what is the derivative of z with respect to x?

Example 5

  • If , what is the derivative of z with respect to x?

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

  • What is given that r = sin(x2 + 1) + cos(x2 + 1)?

Example 15

  • What is if p = er2 + 3r?

Example 16

  • Find  given that y = ln(z4 + z3).

Example 17

  • Find  given that .

Example 18

  • Find  given that q = 1412sin t.
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