maths help

ted9308

I'm having problems with differentiation help needed with the following and explanations explaining ur answer
(i) if x=k(titha -sin titha)and y=k (1 - cos titha) find dy/dx
(ii) e^-x squared sin x
(iii)x^squarede^5x

gemxpink

(i) If x=k(θ - sinθ) and y=k (1 - cosθ), find dy/dx
(ii) [LATEX]e^-^x^2 sin x[/LATEX]
(iii) [LATEX]x^2 e^5^x[/LATEX]

Just gonna leave that there.

RexMundi

Presuming that I read the questions right, these should be correct.

(i) What you need to know is that dy/dx = dy/dt // dy/dx

y = k(1-cost)
.: = k-kcost

.: dt/dt = ksint

x= k(t-sint)
.:= kt - ksint

.: dx/dt = k - kcost

but dy/dx = dy/dt // dx/dt = ksint/kt-kcost

.: ANS = sint / t - cost

(ii) Both this and the next one require the product rule.

ie. if y = uv

dy/dx = u(dv/dx) + v(du/dx)

.: if y = e^-xx.sinx

dy/dx = e^-xx.cosx - 2xe^-xx.sinx

(iii) if y = xx.e^5x

dy/dx = xx.5e^5x +e^5x.2x

.: ANS = 5x^2.e^5x + 2x.e^5x

brownacid

Just use the product rule on all three cases