A curve has the equation 6x^(3/2) + 5y^2 = 2 (a) By differentiating implicitly, find dy/dx in terms of x and y. (b) Hence, find the gradient of the curve at the point (4, 3).

(a) To differentiate implicitly, differentiate x’s as normal and differentiate y’s with respect to y before multiplying by dy/dx. Therefore the differentiating the curve gives
9x^(1/2) + 10y*(dy/dx) = 0
which can be rearranged to give dy/dx = -9x^(1/2) / 10y
(b) at (4, 3) dy/dx = -94^(1/2) / 103
m^(1/2) is equivalent to √m so
dy/dx = -92 / 103 = -3 / 5

ML
Answered by Matthew L. Maths tutor

3448 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove the identity: sin^2(x)+cos^2(x) = 1


Solve x^2=3(x-1)^2


Solve for 0=<x<360 : 2((tanx)^2) + ((secx)^2) = 1


C and D are two events such that P(C) = 0.2, P(D) = 0.6 and P(C|D) = 0.3. Find P(D|C), P(C’ ∩ D’) & P(C’ ∩ D)


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