Differentiate x^cos(x) and find the derivative of cosec^-1(x)

for part a) let y=xcos(X) , the ln(y)=ln(xcos(X))=cos(x)ln(x), thus d/dx (ln(y(x)) = d/dx (cos(x)ln(x)), 1/y*dy/dx=cox(x)/x - sinxlnx => solve for dy/dx => y'(x)=xcos(X) (cox(x)/x - sinxlnx) b) d/dx cosec-1(x)= -1/x(x-1)1/2 this is shown by setting y as the function, rearrange for x then doing implict differentiation to solve for dy/dx in terms of y, then use the defenintions of sine to express in terms of x

Answered by Hari P. Maths tutor

7258 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

solve 4^xe^(7x+5) = 21


d/dx[sin(x) + cos(x)]


differentiate y=8x^3 - 4*x^(1/2) + (3x^2 + 2)/x


What is the natural logarithm?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences