Derivative of sin(x) and cos(x) by definition of derivative and Taylor expansion
100777
Finding the derivatives of sin(x) and cos(x)
156536
Defining functions as derivatives
85085
Simplifying the derivative of $|x|$
6465
How to prove periodicity of $\sin(x)$ or $\cos(x)$ starting from the Taylor series expansion?
137550
Finding the derivatives of inverse functions at given point of c
21203
An intuitive explanation of the Taylor expansion
123476
Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
20280
Proving that expression is equivalent to the definition of derivative
80164
Taylor expansion of a function containing QPochhammer[q, q, n]
33396
Generalizing a Trig Identity
157211
Find the derivative of the inverse of this real function $f(x) = 2x + \cos(x)$
92627
How do we know the Taylor expansion for $e^x$ works for all $x$? Or that it's analytic?
128795
$n$th derivative of $e^x \sin x$
80680
General term of Taylor Series of $\sin x$ centered at $\pi/4$
105999
An application of derivatives problem- to show that $f(x+2)-f(x)>2$ for $f(x)=x\cos(1/x)$
56712
How can I find the domain and derivative of the function?
4956
Connection between Fourier transform and Taylor series