Find the following a ddx x4 b ddx 9x13 c ddw 5w4 d ddx cx2 e

Find the following: a) d/dx (-x^-4) b) d/dx 9x^1/3 c) d/dw 5w^4 d) d/dx cx^2 e) d/dy aub f) d/dy - au^-b

Solution

a ) d/dx(-x^-4) = - d/dx(x^-4) [since,d/dx(-f(x) = -d/dx(f(x) ]

= - (-4).x^-4-1 [ d/dx(xⁿ) = nx^n-1 ]

   = 4x^-5

b ) d/dx(9x^1/3) = 9 d/dx(x^1/3) [ since ,d/dx(af(x)) = a d/dx(f(x)) ]

= 9 .1/3.x^(1/3)-1    [ d/dx(xⁿ) = nx^n-1 ]

= 3x^-2/3

c ) d/dw(5w⁴) = 5d/dw(w⁴) [ since ,d/dw(af(w)) = a d/dx(f(w)) ]

= 5.4.w^4-1   [ d/dw(wⁿ) = nw^n-1 ]

= 20w³

d ) d/dx(cx²) = c d/dx(x²)    [ since ,d/dx(af(x)) = a d/dx(f(x)) ]

= c.2.x^2-1    [ d/dx(xⁿ) = nx^n-1 ]

= c.2x

= 2xc

e ) d/du(aub) = ab.d/du(u)

= ab.1

= ab