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EXAMPLE 7Using the Power Rule for Functions to Find a Derivative

  1. (a) If f(x)=(3x3)5, then f(x)=ddx(3x3)5=Power Rulefor Functions5(3x3)51ddx(3x3)=5(3x3)6(3x2)=15x2(3x3)6=15x2(3x3)6
  2. (b) If f(θ)=cos3θ, then f(θ)=(cosθ)3, and f(θ)=ddθ(cosθ)3=Power Rulefor Functions3(cosθ)31ddθcosθ=3cos2θ(sinθ)=3cos2θsinθ