Differentiate y=(x^2+5)^7

In this example instead of multiplying out 7 brackets it is useful to use the chain rule, which is used to differentiate the composition of more than one function. If we let what is inside the bracket equal u, then u=x^2+5, and y=u^7. The chain rule states that dy/dx=du/dxdy/du, so we simply differentiate both functions and multiply them: remembering that to differentiate x^n we do nx^(x-1), du/dx=2x (as constants disappear) and dy/du=7u^6. Therefore dy/dx=2x7u^6. Now all that is left is to plug the expression for u back in to get dy/dx=2x*7(x^2+5)^6, and simplify to get dy/dx=14x(x^2+5)^6. It is simplest to leave it in this form.

RB
Answered by Rachel B. Maths tutor

5952 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Show that r^2(r + 1)^2 - r^2(r - 1)^2 ≡ 4r^3.


Solve the simultaneous equations: ...


The polynomial p(x) is given by p(x) = x^3 – 5x^2 – 8x + 48 (a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x). [2 marks] (ii) Express p(x) as a product of three linear factors. [3 marks]


A curve C has equation y = (2 - x)(1 + x) + 3 . A line passes through the point (2, 3) and the point on C with x-coordinate 2 + h . Find the gradient of the line, giving your answer in its simplest form.


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences