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:

If a=3a=3, b=7b=7 and c=−5c=-5, verify the following property and identify the name of property. \newlinea×(b+c)=a×b+a×ca \times (b+c) = a \times b + a \times c

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. If a=3a=3, b=7b=7 and c=−5c=-5, verify the following property and identify the name of property. \newlinea×(b+c)=a×b+a×ca \times (b+c) = a \times b + a \times c
  1. Differentiate x4x^4: Differentiate each term separately.\newlineddx(x4)=4x3\frac{d}{dx}(x^{4}) = 4x^{3}
  2. Chain rule for ln⁡(2x)\ln(2x): Use the chain rule for ln⁡(2x)\ln(2x), where u=2xu=2x and the derivative of ln⁡(u)\ln(u) is 1u\frac{1}{u}.ddx(ln⁡(2x))=ddu(ln⁡(u))⋅ddx(2x)=12x⋅2=1x\frac{d}{dx}(\ln(2x)) = \frac{d}{du}(\ln(u)) \cdot \frac{d}{dx}(2x) = \frac{1}{2x} \cdot 2 = \frac{1}{x}
  3. Derivative of exe^x: The derivative of exe^{x} is exe^{x}.\newlineddx(ex)=ex\frac{d}{dx}(e^{x}) = e^{x}
  4. Combine derivatives: Combine the derivatives.\newline(d)/(dx)(x4+ln⁡(2x)+ex)=4x3+1x+ex(d)/(dx)(x^{4}+\ln(2x)+e^{x}) = 4x^{3} + \frac{1}{x} + e^{x}

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 7 months 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 8 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 8 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 8 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 8 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 8 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 8 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 7 months 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 8 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 9 months ago

View all (358)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant