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Derivatives of trig, exponential and log functions worksheets Grade 12

Differentiate sin, cos, eˣ and ln x, with the chain and product rules.

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How to do it

(sin x)′ = cos x, (cos x)′ = −sin x, (eˣ)′ = eˣ, (ln x)′ = 1 ÷ x. Use the chain and product rules with them.

f(x)=x2 sin⁡xf′(x)=2x sin⁡x+x2 cos⁡xf(x) = x^{2}\ \sin x\quad f'(x) = 2x\ \sin x + x^{2}\ \cos x
product rule: (x2)′ sin⁡x+x2(sin⁡x)′\text{product rule: }(x^{2})'\ \sin x + x^{2} (\sin x)'
f′(x)=2x sin⁡x+x2 cos⁡xf'(x) = 2x\ \sin x + x^{2}\ \cos x

Example problems

  1. f(x)=x2exf′(x)=f(x) = x^{2}e^{x}\quad f'(x) =
  2. f(x)=x2 sin⁡xf′(x)=f(x) = x^{2}\ \sin x\quad f'(x) =
  3. f(x)=e2xf′(x)=f(x) = e^{2x}\quad f'(x) =
  4. f(x)= sin⁡(5x)f′(x)=f(x) =\ \sin (5x)\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