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:

g(x)=(x-6)^(2)

22. g(x)=(x−6)2 g(x)=(x-6)^{2}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives using the chain rule IIright chevron icon

Full solution

Q. 22. g(x)=(x−6)2 g(x)=(x-6)^{2}
  1. Identify Function: Identify the function to differentiate.\newlineg(x)=(x−6)2g(x) = (x - 6)^2
  2. Apply Power Rule: Apply the power rule for differentiation: (ddx)[un]=n⋅u(n−1)⋅(dudx)(\frac{d}{dx})[u^n] = n\cdot u^{(n-1)}\cdot(\frac{du}{dx}).g′(x)=2⋅(x−6)2−1⋅(ddx)(x−6)g'(x) = 2\cdot(x - 6)^{2-1}\cdot(\frac{d}{dx})(x - 6)
  3. Differentiate Inside Function: Differentiate the inside function (x−6)(x - 6).(ddx)(x−6)=1−0(\frac{d}{dx})(x - 6) = 1 - 0
  4. Simplify Derivative: Simplify the derivative.\newlineg′(x)=2⋅(x−6)1⋅1g'(x) = 2\cdot(x - 6)^1\cdot1\newlineg′(x)=2⋅(x−6)g'(x) = 2\cdot(x - 6)

More problems from Find derivatives using the chain rule II

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 (17)