Derivative of Reciprocal (1/f)
Read this topicExplanations 4
- This explanation derives a formula for the derivative of 1f(x)\frac{1}{f(x)}f(x)1 using a trick with the product rule---with a caveat mentioned at the end. It is also possible …
By Ray Li, Victor Wang, Joshua Siktar, Ahaan Rungta, Eric Zhang, Moor Xu, Alex Federspiel
- Explanation #200
By Kevin Ren, Eric Zhang, Expii Team
- We can derive a formula for the derivative of a reciprocal with the Quotient Rule: ddx(1f(x))=f(x)ddx(1)−1ddxf(x)f(x)2=\frac{d}{dx}\left(\frac{1}{f(x)}\right) = \frac{f(x)\frac{…
By Joshua Siktar
- One nice way of deriving the product rule for the reciprocal of a function fff is to directly use the limit definition of a derivative, and then use some easy manipulations: ddx…
By Sujay Kazi
Problems 7
- What is the derivative of f(x)=1x2+1f(x) = \frac1{x^2+1}f(x)=x2+11?
- What is the derivative of 15x−1\dfrac1{5x-1}5x−11
- What is the derivative of 14x10\dfrac1{4x^{10}}4x101
- What is the derivative of 12x−7\dfrac1{\sqrt{2x-7}}2x−71
- What is the derivative of 1(((x+3)+2)2+1)3\frac1{\left(\left(\left(x+3\right)+2\right)^2+1\right)^3}(((x+3)+2)2+1)31
- What is the derivative of 13x+1+2x\frac1{\sqrt{\sqrt{3x+1}+2x}}3x+1+2x1
- What is the derivative of 1(((x2)3)4)5\frac1{\left(\left(\left(x^2\right)^3\right)^4\right)^5}(((x2)3)4)51