Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

(a^(2)-ab+ab^(2))/(a^(2)-b^(2)+ab^(2)+b^(3))

a2−ab+ab2a2−b2+ab2+b3 \frac{a^{2}-a b+a b^{2}}{a^{2}-b^{2}+a b^{2}+b^{3}}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives of using multiple formulaeright chevron icon

Full solution

Q. a2−ab+ab2a2−b2+ab2+b3 \frac{a^{2}-a b+a b^{2}}{a^{2}-b^{2}+a b^{2}+b^{3}}
  1. Identify Factors: Identify common factors in the numerator and the denominator.\newlineNumerator: a2−ab+ab2=a(a−b+ab)a^2 - ab + ab^2 = a(a - b + ab)\newlineDenominator: a2−b2+ab2+b3=(a2−b2)+ab2+b3=(a−b)(a+b)+ab2+b3a^2 - b^2 + ab^2 + b^3 = (a^2 - b^2) + ab^2 + b^3 = (a - b)(a + b) + ab^2 + b^3
  2. Factorize Denominator: Factorize the denominator further.\newlineDenominator: (a−b)(a+b)+ab2+b3=(a−b)(a+b)+b(ab+b2)=(a−b)(a+b+b2)(a - b)(a + b) + ab^2 + b^3 = (a - b)(a + b) + b(ab + b^2) = (a - b)(a + b + b^2)

More problems from Find derivatives of using multiple formulae

Question
Find the derivative of f(x) f(x) .\newlinef(x)=cos⁡(x) f(x) = \cos(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡(x) f(x) = \tan(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ex f(x) = e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ln⁡(x) f(x) = \ln(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=xex f(x) = x e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=exx f(x) = \frac{e^x}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) . \newline f(x)=e(x+1) f(x) = e^{(x + 1)} \newline f′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=x+3 f(x) = \sqrt{x+3} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of g(x) g(x). \newline g(x)=ln⁡(2x) g(x) = \ln(2x) \newline g′(x)= g^{\prime}(x) = ______
Get tutor helpright-arrow

Posted 3 months ago

View all (665)