Differentiate (2^x)(5x^2+5x)^2.

This is a relatively difficult equation to differentiate as there are various parts to consider.Firstly, we will let u=2^x and v=(5x^2+5x)^2 in the product rule. Then the differential of u is (2^x)ln(2). We must remember how to differentiate exponential here where the exponent is a variable.Then the differential of v is 2(10x+5)(5x^2+5x) by using the chain rule. If we substitute the correct values into the product rule equation we get an answer of
2(2^x)(10x+5)(5x^2+5x)+(2^x)ln(2)(5x^2+5x)^2.
No need to simplify this.

GH
Answered by George H. Maths tutor

3417 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would you derive y = function of x; for example: y = 3x^3 + x^2 + x


Integrate 3x^2+cos(x) with respect to x


Express 3/2x+3 – 1/2x-3 + 6/4x^2-9 as a single fraction in its simplest form.


Integrate 2x^5 - 1/4x^3 - 5


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