I understand that when using standard Maclaurin series (e.g. e^x=1+x+x^(2)/(2!)+... , we can substitute x with other functions such as z=x^2 to transform the standard Maclaurin series into e^(x^2)=1+x^2+x^(4)/(2!)+...Why doesn't this require a (dz)/(dx)=2x component in the expansion since the standard Maclaurin series are derived from differentiation of the original term.

What is the derivative of the work function?

How to use implicit differentiation to find ${\displaystyle \frac{dy}{dx}}$ given ${\displaystyle 3x^2+3y^2=2}$?

How to differentiate $y=\log <!--\; \; -->x^2$?

The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_1{e}^x+c_2{e}^{2x}$
B) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{3x}$
C) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{-<!--\; -\; -->2x}$
D) $c_1{e}^{-<!--\; -\; -->2x}+c_2{2}^{-<!--\; -\; -->x}$

How to find instantaneous velocity from a position vs. time graph?

How to implicitly differentiate ${\displaystyle \sqrt{xy}=x-2y}$?

What is 2xy differentiated implicitly?

How to find the sum of the infinite geometric series given ${\displaystyle 1+\frac{2}{3}+\frac{4}{9}+...}$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1

What is the derivative of ${\displaystyle \frac{x+1}{y}}$?

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

How to find the volume of a cone using an integral?

What is the surface area of the solid created by revolving ${\displaystyle f\left(x\right)=e^{2-x},x\in [1,2]}$ around the x axis?

How to differentiate ${\displaystyle x^{\frac{2}{3}}+y^{\frac{2}{3}}=4}$?

The differential coefficient of $\sec \left({\tan }^{-1}\left(x\right)\right)$.