The statement illustrates a failure to apply the chain rule: a corrected version would be $$\frac {d} {dx}\left (\pi^2\right)=2\pi\cdot\frac {d\pi} {dx}=2\pi\cdot 0=0\;.$$ Of course this is doing far …

Oct 16, 2012 · I'm trying to show that the derivative of $\sin\theta$ is equal to $\pi/180 \cos\theta$ if $\theta$ is measured in degrees. The main idea is that we need to convert $\theta$ to …

Derivative of capital Pi and Sigma Ask Question Asked 5 years, 11 months ago Modified 5 years, 11 months ago

The second derivative $\frac {d^2V} {dr^2} = -6r\pi$ The formula and derivatives are both correct, however, my original attempt at them was the exact same apart from the exclusion of $\pi$.

Jun 26, 2015 · I'm still struggling to understand why the derivative of sine only works for radians. I had always thought that radians and degrees were both arbitrary units of measurement, and …

Jul 10, 2015 · You mentioned that it's true for the 2-sphere, and for the 3-sphere, but it should be noted that it is also true for the 1-sphere, which is the interval from -r to r, which has 1-volume …

Mar 28, 2016 · No, you don't get the derivative at $\pi/2$; however, the cotangent function is continuous at $\pi/2$ and $$ \lim_ {x\to\pi/2}\cot' (x)= \lim_ {x\to\pi/2}-\frac {1} {\sin^2 (x)}=-1 $$ …

Sep 24, 2019 · But clearly, $e^ {i\pi}$ is a constant, so it's derivative is $0.$ This result clearly follows from the definition of derivative. $dy\over dx$ is the rate of change of $y$ with respect …

Jun 14, 2019 · How do you prove the power rule can be applied for the derivative of $$x^\\pi?$$Since the power is an irrational number, how to use the binomial theorem in this …

Aug 4, 2017 · Consider a sphere for example. It's volume is calculated by the formula: $\frac 4 3 \pi r^3$ The derivative of that is $4\pi r^2$ which represents the sphere's surface area. The …