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The chain rule worksheets Grade 12

Differentiate composite functions: the outside, then times the inside's derivative.

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How to do it

Derivative of the outside, keeping the inside, times the derivative of the inside.

f(x)=2xf′(x)=12xf(x) = \sqrt{2x}\quad f'(x) = \dfrac{1}{\sqrt{2x}}
derivative of √u is 1÷(2√u), times u′\text{derivative of }\surd u\ \text{is }1 \div (2\surd u),\ \text{times }u'
222x=12x\dfrac{2}{2\sqrt{2x}} = \dfrac{1}{\sqrt{2x}}

Example problems

  1. f(x)=6x+4f′(x)=f(x) = \sqrt{6x + 4}\quad f'(x) =
  2. f(x)=6x+2f′(x)=f(x) = \sqrt{6x + 2}\quad f'(x) =
  3. f(x)=(−3x2−3)6f′(x)=f(x) = (-3x^{2} - 3)^{6}\quad f'(x) =
  4. f(x)=4x−4f′(x)=f(x) = \sqrt{4x - 4}\quad f'(x) =

Limits and derivatives

  1. Evaluating limits
  2. The power rule for derivatives
  3. The product rule
  4. The quotient rule
  5. The chain rule
  6. Derivatives of trig, exponential and log functions
  7. Equation of a tangent line
  8. Derivatives as rates of change
  9. Finding maximum and minimum points