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Use the differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.

f(x)=(3xx)-2

Short Answer

Expert verified

The derivative of the given function is-13x4.

Step by step solution

01

Step 1. Given Information

The given expression isf(x)=(3xx)-2.

02

Step 2. Simplify the function

Simplify the function.

f(x)=3x32-2=3-2x-3=x-39

03

Step 2. Find the derivative

  • Apply the constant multiple rule of derivative,(kf)'(x)=kf'(x).

f'(x)=ddx(x-39)=19ddxx-3

  • Apply the power rule of derivative, (xn)'=nxn-1.

f'(x)=19(-3x-4)=-x-43=-13x4

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