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The power rule for derivatives worksheets Grade 12

Differentiate powers of x, including roots and fractions written as powers.

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Free · Worked example · 12 problems · Answer key · US Letter

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How to do it

d/dx xⁿ = nxⁿ⁻¹. Write roots and fractions as powers first. The derivative of a constant is 0.

f(x)=7x3f′(x)=−21x4f(x) = \dfrac{7}{x^{3}}\quad f'(x) = \dfrac{-21}{x^{4}}
write it as 7x−3\text{write it as }7x^{-3}
derivative −21x−4\text{derivative }-21x^{-4}the power rule works for negative powers
f′(x)=−21x4f'(x) = \dfrac{-21}{x^{4}}

Example problems

  1. f(x)=−9x3f′(x)=f(x) = \dfrac{-9}{x^{3}}\quad f'(x) =
  2. f(x)=−4x4f′(x)=f(x) = \dfrac{-4}{x^{4}}\quad f'(x) =
  3. f(x)=−5x4−3x3−8x2+4xf′(x)=f(x) = -5x^{4} - 3x^{3} - 8x^{2} + 4x\quad f'(x) =
  4. f(x)=xf′(x)=f(x) = \sqrt{x}\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