Trig Functions problem! (1 Viewer)

[RHINO7]

Stuck on two questions-

i) Find the derivative of cos x sin^4x


ii) Find the exact area bounded by the curve y=cos 3x, the x-axis and the lines x=0 and x=pi/12.

 

[watatank]

Stuck on two questions-

i) Find the derivative of cos x sin^4x


ii) Find the exact area bounded by the curve y=cos 3x, the x-axis and the lines x=0 and x=pi/12.

i) its just the product rule and chain rule

= sinx*(sinx)^4 + cosx * 4(sinx)^3*cosx

= (sinx)^5 +4(sinx)^3(cosx)^2

ii) integral of cos 3x = (1/3)sin3x with limits from 0 to pi/12. you should be able to work it out from here.

 

[Getteral09]

HEy i have a maths problems that i can't seem to figure it out.

" Find the gradient of the tangent at the point indicated: c) y = tan x at x=0"

And i seem to end up with At x=0, y'= sec^2x0 which equals to zero?
How come the answer says 1??

Can anyone plz explain this theory to me?>?

 

[watatank]

y = tanx
y' = (secx)^2

(secx)^2 = 1/(cosx)^2


cos 0 = 1

when x = 0,
y' = 1

 

[Getteral09]

THanks heaps.