Find the derivatives of the functions z=\frac{4-3x}{3x^{2}+x}

Haven

Haven

Answered question

2021-10-20

Find the derivatives of the functions
z=43x3x2+x

Answer & Explanation

aprovard

aprovard

Skilled2021-10-21Added 94 answers

Step 1
The derivative of a function is the rate of change of the function with respect to the function variable. The derivative of a function of the form f(x)g(x) can be calculated using the quotient rule, which is given by,
(f(x)g(x))=g(x)f(x)f(x)g(x)(g(x))2
Step 2
Therefore, the derivative of the function z=43x3x2+x is given by,
z=d(43x3x2+x)dx
=(3x2+x)(d(43x)dx)(43x)(d(3x2+x)dx)(3x2+x)2
=(3x2+x)(3)(43x)(6x+1)(3x2+x)2
=9x23x(24x+418x23x)(3x2+x)2
=9x23x24x4+18x2+3x(3x2+x)2
=9x224x4(3x2+x)2
Therefore, the derivative of the function is 9x224x4(3x2+x)2

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