Power Rule for Derivatives: Real Exponents
Read this topicExplanations 10
- The full power rule is as follows.The derivative of b∗axb*a^xb∗ax with respect to aaa, is bxax−1bxa^{x-1}bxax−1. We can see why this is true when we take a look at the limit def…
By Siddharth Namachivayam, Joshua Siktar, Victor Wang
- There is actually a way of showing that ddx(xr)=rxr−1\frac{d}{dx}(x^r) = r x^{r-1}dxd(xr)=rxr−1 for all rrr directly, without worrying about whether rrr is positive or an integ…
By Misha Lavrov, Anthony Wu, Moor Xu
- SQUAD first form of PowerRule was used by Bonaventura Cavalieri in the 17 century and was later improved by Newton and Leibniz who was both working individually. The power rule …
By Howei, giovanni evans
- The power rule for derivatives is that if the original function is xnx^nxn, then the derivative of that function is nxn−1n x^{n-1}nxn−1. To prove this, you use the limit definit…
By Mohsin Sarwar, Cassie Taylor, Po-Shen Loh, xiao hua, Anthony Wu
- The power rule is used to distinguish the form of functions f(x) = x^r, whenever r is the real number. The derivative of a power x is equal to the product of exponent times x wi…
By Cindy Zheng
- Congratulations, you have just learned the Full Power Rule! Now you can do every single problem on here, best of luck!
By Freya Edholm
- (Video) Power Rule with Post-Its by Grace Carey This explanation will focus on how to apply the Power Rule in practice. We will focus more on the method than theory, which is co…
By Grace Carey, Alex Federspiel
- (Video) Using the Power Rule to Find Derivatives by PatrickJMT Here's a video by patrickJMT showing you how to use the power rule to solve derivative instead of that long and an…
By Alex Federspiel
- (Videos) Power Rule and Derivatives by PatrickJMT Here's a video by patrickJMT where he goes over some examples of finding the derivative using the power rule. Recall that the p…
By Alex Federspiel
- (Video) Solving Every Derivative Ever by PatrickJMT Okay, maybe it's not EVERY derivative ever but here's a video by patrickJMT going over different derivatives for a whopping 3…
By Alex Federspiel
Problems 12
- What is ddx(x)\frac{d}{dx} \left(\sqrt{x}\right)dxd(x)?
- If f(x)=x2.687f(x)=x^{2.687}f(x)=x2.687, what is f′(x)f'(x)f′(x)?
- If f(x)=xaf(x)=x^af(x)=xa and a∈Ra\in\mathbb{R}a∈R then find the derivative function f′(x)f'(x)f′(x).
- Find the derivative of f(x)=2x23f(x)=2x^{23}f(x)=2x23
- Find the derivative of f(x)=x3+2xf(x)=x^3+\frac2{x}f(x)=x3+x2
- Find the derivative of f(x)=x544f(x)=\sqrt[4]{x^{\frac54}}f(x)=4x45
- Find the derivative of f(x)=x7+8x5−6x3+3f(x)=x^7+8x^5-6x^3+3f(x)=x7+8x5−6x3+3
- Find the derivative of f(x)=18f(x)=\sqrt{18}f(x)=18
- Find the derivative of f(x)=x(2x2+4x)f(x)=x\left(2x^2+\frac4x\right)f(x)=x(2x2+x4)
- What values of xxx does the function f(x)=13x3−2x2+4x−37πf(x)=\frac13x^3-2x^2+4x-37\pif(x)=31x3−2x2+4x−37π have a horizontal tangent?
- Find the derivative of f(x)=(13x273)3f(x)=\left(\frac13x^{\frac{27}3}\right)^3f(x)=(31x327)3
- Find the derivative of f(x)=xf(x)=\sqrt{\sqrt{x}}f(x)=x