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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)=x7-3x5+41-3x4

Short Answer

Expert verified

The derivative of the function isf'(x)=(7x6-15x4)(1-3x4)-(x7-3x5+4)(-12x3)(1-3x4)2.

Step by step solution

01

Step 1. Given Information

The given function isf(x)=x7-3x5+41-3x4.

02

Step 2. Find the derivative

Apply the quotient rule of derivative, (fg)'(x)=f'(x)g(x)-f(x)g'(x)(g(x))2.

f'(x)=ddx(x7-3x5+4)·(1-3x4)-(x7-3x5+4)ddx(1-3x4)(1-3x4)2=(7x6-15x4)(1-3x4)-(x7-3x5+4)(-12x3)(1-3x4)2

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