Find the Derivative - d/dx (x^2)/(x^2-25)

Problem

d()/d(x)(x2)/(x2−25)

Solution

1. Identify the rule needed for differentiation. Since the expression is a fraction of two functions, apply the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator functions. Let u=x2 and v=x2−25

3. Differentiate the individual components.

d(x2)/d(x)=2*x

d(x2−25)/d(x)=2*x

4. Substitute these into the quotient rule formula.

d()/d(x)(x2)/(x2−25)=((x2−25)*(2*x)−(x2)*(2*x))/((x2−25)2)

5. Expand the terms in the numerator.

d()/d(x)(x2)/(x2−25)=(2*x3−50*x−2*x3)/((x2−25)2)

6. Simplify the numerator by combining like terms.

d()/d(x)(x2)/(x2−25)=(−50*x)/((x2−25)2)

Final Answer

d()/d(x)(x2)/(x2−25)=−(50*x)/((x2−25)2)

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