How do I use the chain rule to differentiate polynomial powers of e?

e(x^2+2)=f(x)=y

Is the equation we will use to demonstrate correct use of the chain rule.

The equation at the core of the chain rule is:

dy/dx=dt/dx*dy/dt

Seeing that dt as a numerator and dt as a denominator are both present in the equation allows us to cancel dt from the equation.

When using the chain rule, firstly, we must express f(x) using a simpler power of e, to do this we set t equal to x2+2, giving us the following equalities.

t=x2+2

y=et

From our differentiation rules we know that:

y=et

dy/dt=et

And:

t=x2+2

dt/dx=2x

Finally, we substitute into dy/dx=dt/dx*dy/dt 

(dy/dt)*(dt/dx)=dy/dx

(e(x^2+2))*(2x)=dy/dx

y=e(x^2+2)

dy/dx=2xe(x^2+2)

JO
Answered by Joshua O. Maths tutor

5325 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Use integration by parts to evaluate: ∫xsin(x) dx.


Solve the inequality x^2 – 5x – 14 > 0.


A curve has an equation of y = 20x - x^2 - 2x^3, with one stationary point at P=-2. Find the other stationary point, find the d^2y/dx^2 to determine if point P is a maximum or minium.


When is an arrangement a combination, and when a permutation?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning