Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative using the definition
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
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We can factor the fourth degree trinomial $x^4+6x^2+9$ by applying the substitution: $y=x^2$
Learn how to solve definition of derivative problems step by step online.
$derivdef\left(\frac{x^3+x-1}{y^2+6y+9}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (x^3+x+-1)/(x^4+6x^2+9) using the definition. We can factor the fourth degree trinomial x^4+6x^2+9 by applying the substitution: y=x^2. Find the derivative of \frac{x^3+x-1}{y^2+6y+9} using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \frac{x^3+x-1}{y^2+6y+9}. Substituting f(x+h) and f(x) on the limit, we get. Combine \frac{\left(x+h\right)^3+x+h-1}{y^2+6y+9}-\frac{x^3+x-1}{y^2+6y+9} in a single fraction. Divide fractions \frac{\frac{\left(x+h\right)^3+h-x^3}{y^2+6y+9}}{h} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.